This specification is a revision of the last-call working draft dated
1998-10-30 incorporating suggestions received in review
comments and further deliberations of the W3C RDF Schema Working Group.
The detailed differences
are available for reviewers to compare.

The Working Group anticipates no further substantial changes to
this specification. We encourage active implementation to test this
specification during the Proposed Recommendation review period.

Publication as a Proposed Recommendation does not imply endorsement
by the W3C membership. This is a draft document
and may be updated, replaced or obsoleted by other documents at any
time. It is inappropriate to cite W3C Drafts as other than
"work in progress".

The Resource Description Framework is part of the W3C
Metadata Activity. The goal of this activity, and of RDF specifically,
is to produce a language for the exchange of machine-understandable descriptions
of resources on the Web. A separate specification describes the
data model and syntax for the interchange of metadata using RDF.

Note: The HTML source of this document contains embedded RDF and
will therefore not validate against the HTML4.0 DTD. A solution for those
requiring DTD-style validation services may come from future W3C
work.

RDF Schemas

1. Introduction

The Resource Description Framework (RDF) is a foundation for processing
metadata; it provides interoperability between applications
that exchange machine-understandable information on the Web. RDF emphasizes
facilities to enable automated processing of Web
resources. RDF can be used in a variety of application areas; for example:
in resource discovery to provide better search engine
capabilities, in cataloging for describing the content and content
relationships available at a particular Web site, page, or digital
library, by intelligent software agents to facilitate knowledge sharing and
exchange, in content rating, in describing collections of
pages that represent a single logical "document", for describing
intellectual property rights of Web pages, and for expressing the
privacy preferences of a user as well as the privacy policies of a Web site.
RDF with digital signatures will be key to building the
"Web of Trust" for electronic commerce, collaboration, and other
applications.

Descriptions used by these applications can be modelled as
relationships among Web resources. The RDF data model, as specified in
[RDFMS], defines a simple model for describing
interrelationships among resources in terms of named properties and values.
RDF properties may be thought of as attributes of resources and in this sense
correspond to traditional attribute-value pairs. RDF properties also
represent relationships between resources. As such, the RDF data model can
therefore resemble an entity-relationship diagram. The RDF data model,
however, provides no mechanisms for declaring these properties, nor does it
provide any mechanisms for defining the relationships between these
properties and other resources. That is the role of RDF Schema.

Resource description communities require the ability to say certain things
about certain kinds of resources. For describing bibliographic resources,
for example, descriptive attributes including "author", "title", and
"subject" are common. For digital certification, attributes such as
"checksum" and "authorization" are often required. The declaration
of these properties (attributes) and their corresponding semantics are defined in the
context of RDF as an RDF schema. A schema defines not only the
properties of the resource (Title, Author, Subject, Size, Color, etc.) but
may also define the kinds of resources being described (books, Web pages,
people, companies, etc.).

This document does not specify a vocabulary of descriptive elements
such as "author". Instead, it specifies the mechanisms
needed to define such elements, to define the classes of resources they
may be used with, to restrict possible combinations of classes and relationships,
and to detect violations of those restrictions. Thus, this document
defines a schema specification language. More succinctly, the
RDF Schema mechanism provides a basic type system for use in RDF
models. It defines resources and properties such as Class and
subClassOf that are used in specifying application-specific schemas.

The typing system is specified in terms of the basic RDF data model - as
resources and properties.
Thus, the resources constituting this typing system become
part of the RDF model of any description that uses them. The schema
specification language is a declarative representation language influenced by ideas from knowledge
representation (e.g. semantic nets, frames, predicate logic) as well as
database schema specification languages (e.g. NIAM)
and graph data models. The RDF schema specification language is less expressive, but much
simpler to implement, than full predicate calculus languages such as
CycL[CycL] and KIF [KIF].

RDF and the RDF Schema language were also based on metadata research
in the the Digital Library community. In particular, RDF adopts a
modular approach to metadata along the lines of the Warwick Framework
[WF]. RDF represents an evolution of the Warwick
Framework model in that the Warwick Framework allowed each
metadata vocabulary to be represented in a different syntax. In RDF,
all vocabularies are expressed within a single well defined model and
syntax. This allows for a finer grained mixing of machine-processable
vocabularies, and addresses the need [EXTWEB] to
create metadata in which statements can draw upon multiple vocabularies
that are managed in a decentralised fashion by various communities of
expertise.

RDF Schemas might be contrasted with XML Document Type
Definitions (DTDs). Unlike an XML DTD, which gives specific
constraints on the structure of a document, an RDF Schema
provides information about the interpretation of the statements
given in an RDF data model. The RDF/XML syntax itself provides
considerable flexibility in the syntactic expression of the data
model. A syntactic schema alone is not sufficient for RDF
purposes. RDF Schemas may also specify consistency constraints
that should be followed by these data models.

1.1 Scope

The RDF Schema specification is not aimed at theoretical issues, but at solving a
small number of immediate problems. Its creators expect that other problems (some of
which are illustrated in the examples below) will share similar characteristics
and that they also may be able to use the basic classes described in this
specification.

The RDF Schema specification was directly influenced by consideration
of the following problems:

1.1.1 Platform for Internet Content Selection (PICS)

The RDF Model and Syntax is adequate to represent PICS labels
[PICS], however it does not provide a general-purpose
mapping from PICS rating systems into an RDF representation. One such
mapping is presented in section 7.

1.1.2 Simple Web Metadata

One obvious application for RDF is in the description of Web pages.
This is one of the basic functions of the Dublin Core [DC]
initiative. The Dublin Core is a set of 15 elements believed to be broadly
applicable to describing Web resources to enable their discovery. The Dublin
Core has been a major influence on the development of RDF. An important
consideration in the development of the Dublin Core was to not only allow simple
descriptions, but also to provide the ability to qualify descriptions in
order to provide both domain specific elaboration and descriptive precision.

The RDF Schema specification provides a machine-understandable
system for defining 'schemas' for descriptive vocabularies like the Dublin
Core. It allows designers to specify classes of Resource types and properties
to convey descriptions of those classes, and constraints on the allowed
combinations of classes, properties, and values.

An initial schema for the simple Dublin Core is provided in Appendix B.
This schema defines the 15 elements as properties, and gives a description
of their purpose. Despite the simplicity of the definition, it is believed
that this schema serves as the foundation for more elaborate definitions.
Future extensions to the Dublin Core are likely to specify the structure of the
values of the properties, which will involve defining classes, the properties
that apply to those classes, and some constraints on the property values.
In order for browsers and authoring tools to understand and enforce these
constraints, this information should be machine understandable. This document
provides a machine understandable schema language for expressing such definitions
and constraints.

1.1.3 Sitemaps and other such Navigation Tools

A sitemap is a hierarchical description of a Web site. A subject taxonomy
is a classification system that might be used by content creators or trusted
third parties to organise or classify Web resources.
The RDF Schema specification provides a mechanism for defining the vocabularies
needed for such applications.

Thesauri and library classification schemes are well known examples of
hierarchical systems for representing subject taxonomies in terms of the
relationships between named concepts. The RDF Schema specification
provides sufficient resources for creating RDF models that represent the
logical structure of thesauri (and other library classification systems).

1.1.4 P3P

The W3C Platform for Privacy Preferences Project (P3P) requires a grammar
for constructing statements about a site's data collection practices and personal
preferences as exercised over those practices, as well as a syntax for
exchanging structured data. The ability to provide third party assurances (signed
statements) regarding P3P practices is also important. For instance, entities
may wish to certify that P3P practice statements were properly generated
in accordance with industry guidelines, have been audited, or are compliant
with the relevant privacy regulations.

Although personal data collection practices could be described
using an application-specific XML tagset, there are benefits to
using a general metadata model for this data. Using a metadata
schema to describe the formal structure of privacy practice
descriptions will permit privacy practice data to be used along
with other metadata in a query during resource discovery, and will
permit a generic software agent to act on privacy metadata using
the same techniques as used for other descriptive metadata.

1.2 Specifying the Schema

An RDF Schema can be expressed by the data model described in the RDF Model
and Syntax [RDFMS] specification. The schema description
language is simply a set of resources and properties defined by this
specification and implicitly part of every RDF model using this schema
machinery.

This document specifies the RDF Schema mechanism as a set of RDF
resources (including properties), and constraints on their relationships.

1.2.1 Versioning and URI references

The Resource Description Framework is intended to be flexible and easily
extensible; this suggests that a great variety of schemas will be created
and that new and improved versions of these schemas will be a common occurence
on the Web. Since changing the logical structure of a schema risks
breaking other RDF models which depend on that schema, this specification
recommends that a new URI is used whenever an RDF schema is changed.

In effect, changing the RDF statements which constitute a schema creates a
new one; new schema namespaces should have their own URI to avoid
ambiguity. Since an RDF Schema URI unambiguously identifies a single
version of a schema, software that uses or manages RDF (eg. caches)
should be able to safely store copies of RDF schema models for an
indefinite period. The problems of RDF schema evolution share many
characteristics with XML DTD version management and the general problem
of Web resource versioning. A general approach to these issues is beyond
the scope of this specification.

Since each RDF schema has its own unchanging URI, these can be used to
construct unique URI references for the resources defined in a schema. This is
achieved by combining the local identifier for a resource with the URI
associated with that schema namespace. The XML representation of RDF uses
the XML namespace mechanism for associating elements and attributes with
URI references for each vocabulary item used.

Note that the formal URI corresponding to the RDF Schema namespace
has not yet been assigned. For the purposes of this document we use as
a temporary URI the identifier for the working draft of the RDF Schema
specification. The same approach is adopted here for the URI of
the RDF Model and Syntax namespace. Consequently, these URIs will change
in the final version of this specification.

1.2.2 Capitalization Convention

In accord with Appendix C.1 of the RDF Model and Syntax Specification
we adopt the following convention concerning capitalization of
property and class names:

Class names have the first letter capitalized,
e.g., rdfs:Resource. Additional words in
the class name are also capitalized, e.g.,
rdfs:ConstraintProperty.

Property names do not have the first letter capitalized,
e.g., rdfs:domain.
However, additional words in
the name are capitalized,
e.g., rdfs:subClassOf.

2. Classes and Properties

In this section we describe the core RDF Schema. We first define
the type system and then introduce the core classes and properties.

2.1 The Type System

The RDF Schema defined in this specification is a collection of RDF resources
that can be used to describe properties of other RDF resources (including properties)
which define application-specific RDF vocabularies.
The core schema vocabulary is defined in a namespace informally called 'rdfs'
here, and which will be given a formal URI in the final version of this specification.

As described in the RDF Model and Syntax specification, resources may be instances of
one or more classes; this is indicated with the rdf:type
property. Classes themselves are often organised in a hierarchical
fashion, for example the class 'dog' might be considered a sub-class of
'animal' which is a sub-class of 'organism' etc., meaning that any
resource which is of rdf:type 'dog' is ipso facto also of
rdf:type 'animal' and so on. This specification describes a
property, rdfs:subClassOf, to denote such relationships
between classes.

In addition to the rdfs:subClassOf property, this
specification introduces a number of
other resources for making statements about constraints on the consistent use of
properties and classes in RDF data. For example, an RDF schema might describe
limitations on the types of values that are valid for some property, or on the classes
to which it makes sense to ascribe such properties.
This specification gives a mechanism for describing such constraints, but does not
say whether or how an application must process the constraint information.
For example, while an RDF schema may express that a 'Book' may have an 'author' property,
it does not say whether or how an application should act in processing
that information. We expect that different applications will use these
constraints in different ways. e.g., a validator will look for errors,
an interactive editor might suggest legal values.

We anticipate the development of a set of classes corresponding to a
set of "datatypes." This specification does not define datatypes, but does
note that datatypes may be used as the value of the
rdfs:range property.

2.1.1 Figure 1: Classes and Resources as Sets and Elements

Figure 1 illustrates the concepts of class, sub-class, and
resource. A class is depicted by a rounded rectangle, a resource is
depicted by a large dot. In the figure below, arrows are drawn from a
resource to the class it defines. A sub-class is shown by having a rounded rectangle (the
sub-class) completely enclosed by another (the super-class). If a resource
is inside a class, then there exists either an explicit or implicit
rdf:type property of that resource whose value is the resource defining the
containing class. (These properties are shown as arcs in the directed labelled
graph representation in figure 2). The RDF resources depicted in figure 1
are described either in the remainder of this specification, or in the RDF
Model and Syntax specification.

Figure 1: Classes and Resources as Sets and Elements

2.1.2 Figure 2: Class Hierarchy for the RDF Schema

Figure 2 shows the same information about the class hierarchy
as in figure 1, but does so using a "nodes and arcs" graph representation of
the RDF data model.
If a class is a subset of another, then there is an rdfs:subClassOf
arc from the node
representing the first class to the node representing the second. Similarly,
if a Resource was an instance of a Class, then there is an rdf:type
arc from the resource to the node representing the class. (Not all such arcs are shown.
We only show the arc to the most tightly encompassing class, and rely on the transitivity
of the rdfs:subClassOf relation to provide the rest).

Figure 2: Class Hierarchy for the RDF Schema

2.2 Core Classes

The following resources are core classes that are defined as part of the
RDF Schema machinery. Every RDF model that draws upon the RDF
Schema vocabulary namespace (implicitly) includes these.

2.2.1 rdfs:Resource

All things being described by RDF expressions are called resources, and are
considered to be instances of the class rdfs:Resource.
The RDF class rdfs:Resource
represents the set called 'Resources' in the formal model for RDF presented in section 5 of
the Model and Syntax specification [RDFSMS].
This roughly corresponds to the concept of Object in Java.

Note that the class rdfs:Resource
is unrelated to the syntactic attribute 'resource' used in the RDF/XML
serialization syntax (just as the resource 'Description' defined by
the Dublin Core element set is unconnected to the syntactic element
'Description' used in the RDF/XML syntax).

2.2.2 rdf:Property

The class rdf:Property represents the subset of RDF resources that are properties,
i.e., all the elements of the set introduced as 'Properties' in section 5 of the Model
and Syntax specification [RDFSMS].

2.2.3 rdfs:Class

This corresponds to the generic concept of a Type or
Category, similar to the notion of a Class in object-oriented
programming languages such as Java.
When a schema defines a new class, the resource representing that class must
have an rdf:type property whose value is the resource rdfs:Class.
RDF classes can be defined to represent almost anything, such as Web pages, people, document types,
databases or abstract concepts.

2.3 Core Properties

Every RDF model which uses the schema mechanism
also (implicitly) includes the following core properties.
These are instances of the rdf:Property class and provide
a mechanism for expressing relationships between classes and their instances
or superclasses.

2.3.1 rdf:type

This indicates that a resource is a member of a class, and thus has all
the characteristics that are to be expected of a member of that class.
When a resource has an rdf:type property whose value is
some specific class, we say
that the resource is an instance of the specified class. The value of an
rdf:type property for some resource is
another resource which must be an instance of rdfs:Class.
The resource known as rdfs:Class is itself a resource of rdf:typerdfs:Class. Individual classes (for example, 'Dog') will always have an
rdf:type property whose value is rdfs:Class (or some sub-class
of rdfs:Class, as described in section 2.3.2). A resource may be an instance
of more than one class.

2.3.2 rdfs:subClassOf

This property specifies a subset/superset relation between classes.
The rdfs:subClassOf property is transitive.
If class A is a sub-class of some broader class B, and B is a sub-class of
C, then A is also implicitly a sub-class of C. Consequently, resources
that are instances of class A will also be instances of C, since A is a
sub-set of both B and C. Only instances of rdfs:Class can have the
rdfs:subClassOf property and the property value is always of
rdf:typerdfs:Class. A class may be a
sub-class of more than one class.

A class can never be declared to be a sub-class of itself, nor of any
of its own sub-classes. Note that this constraint is not expressible
using the RDF Schema constraint facilities provided below, and so does
not appear in the RDF version of this specification given in Appendix A.

2.3.2.1 Example

This is a very simple example that expresses the following class
hierarchy. We first define a class 'MotorVehicle'. We then define 3
subclasses of 'MotorVehicle', namely 'PassengerVehicle', 'Truck' and
'Van'. We then define a class 'Minivan' which is a sub-class of both
'Van' and 'PassengerVehicle'.

The RDF/XML shown here uses the basic RDF syntax defined in section 2.2.1
of the Model and Syntax specification [RDFMS]. The RDF
syntax also provides (in section 2.2.2) a more compact mechanism for
making statements about the rdf:type of a resource, by
allowing the identifier for a class (eg. 'Van' in the examples below) to
be used directly as an XML element name. For example, <Van
ID="v_323"/> tells us both that there is an resource known as
'v_323' and that it is an instance of the class Van.
Similarly, <rdfs:Class ID="MiniVan"/> might be used
to state that the resource known as MiniVan is itself a
class. For clarity,
these initial examples do not take advantage of the rdf:type
abbreviation mechanism provided by the RDF serialisation syntax. In
general, the XML representation of an RDF schema can make full use of all
the syntactic flexibility of RDF.

2.3.3 rdfs:subPropertyOf

An instance of rdf:Property that is used to specify that one
property is a specialization of another. A property may have
zero, one, or more properties that it is a
specialization of. If some property P2 is a subPropertyOf another more
general property P1, and if a resource A has a P2 property with a value B,
this implies that the resource A also has a P1 property with
value B.

A property can never be declared to be a sub-property of itself, nor of
any of its own sub-properties. Note that this constraint is not
expressible using the RDF Schema constraint facilities provided below,
and so does not appear in the RDF version of this specification given in
Appendix A.

2.3.3.1 Example

If the property biologicalFather is a
sub-property of the broader property biologicalParent, and if Fred is the
biologicalFather of John, then it is implied that Fred is also the
biologicalParent of John.

2.3.4 seeAlso

The property rdfs:seeAlso
specifies a resource that contains information about the subject resource. This
property may be specialized using rdfs:subPropertyOf to more precisely
indicate the nature of the information the object resource has about the
subject resource. The object and the subject resources are constrained only to be instances of the class
rdfs:Resource.

2.3.5 isDefinedBy

The property rdfs:isDefinedBy is a sub-property of
rdfs:seeAlso, and indicates the resource
defining the subject resource. As with rdf:seeAlso, this
property can be applied to any instance of rdfs:Resource and may have
as its value any rdfs:Resource.

The most common anticipated usage is to identify the RDF schema given a
name for one of the properties or classes defined by that schema.
Although XML namespace declarations will typically provide the URI where
RDF
vocabulary resources are defined, there are cases where additional
information is required.

For example, constructs such as <rdfs:subPropertyOf
rdf:resource="http://purl.org/dc/elements/1.0/Creator"/>
do not
indicate the URI of the schema that includes the vocabulary item
Creator (ie., http://purl.org/dc/elements/1.0/).

In such cases, the rdfs:isDefinedBy property can be used to explicitly
represent that
information. This approach will also work when the URIs of the namespace and its
components have no obvious relationship, as would be the case if they
were identified using schemes such as GUIDs or MD-5 hashes.

2.4 RDF and Object Orientation

The RDF Schema type system is similar to the type systems of
object-oriented programming languages such as Java.
However, RDF differs from many such systems in that instead of defining
a class in terms of the properties its instances may have, an RDF schema
will define properties in terms of the classes of resource that they apply
to.
This is the role of the rdfs:domain and
rdfs:range constraints described below. For example, we
could define the "author" property to
have a domain of "Book" and a range of "Literal", whereas a classical
OO system might typically define a class "Book" with a property called
"author" of type "Literal". One benefit of this property-centric
approach is that it is very easy for anyone to say anything they want
about existing resources, which is one of the axioms of the Web.

3. Constraints

An RDF schema can declare constraints associated with classes and properties.
In particular, the concepts of domain and range
are used in RDF schemas to make statements about the contexts in which
certain properties "make sense".

Although the RDF data model does not allow for explicit properties (such
as an rdf:type property) to be ascribed to Literals (atomic values),
we nevertheless consider these entities to be members of classes (e.g.
the string "John Smith" is considered to be a member of the class
rdfs:Literal.)
We expect future work in RDF and XML data-typing to provide
clarifications in this area.

An RDF model that violates any of the consistency
constraints specified in this document is said to be
an inconsistent model. The following constraints are specified:
rdfs:domain and rdfs:range
constraints on property usage, the rule that rdfs:subPropertyOf and
rdfs:subClassOf properties should not form loops, plus any
further consistency constraints defined using the
rdfs:ConstraintResource extensibility mechanism.
Different applications may exhibit different behaviours in the
face of an inconsistent model.

Some examples of constraints include:

That the value of a property should be a resource of a designated class.
This is expressed by the range property. For example, a range
constraint applying to the 'author' property may express that the
value of an 'author' property must be a resource of class 'Person'.

That a property may only be used on resources of a certain class.
For example, that an 'author' property could only originate from a
resource that was an instance of class 'Book'.
This is expressed using the domain property.

RDF schemas can express constraints that relate vocabulary items from
multiple independently developed schemas. Since URI references are used to
identify classes and properties, it is possible to create new properties
whose domain or range is constrained to be a class defined in
another namespace.

The RDF Schema uses the constraint properties to constrain how its
own properties can be used. These constraints are shown below in
figure 3. Nodes with bold outlines are instances of
rdfs:Class.

Figure 3: Constraints in the RDF Schema

3.1 Core Constraints

3.1.1 rdfs:ConstraintResource

This resource defines a sub-class of rdfs:Resource whose
instances are RDF schema constructs involved in the expression of
constraints. The purpose of this class is to provide a mechanism
that allows RDF processors to assess their ability to check the
consistency of an RDF model. Since this specification does not provide a
mechanism for the dynamic discovery of new forms of constraint, an RDF 1.0
processor encountering previously unknown instances of
rdfs:ConstraintResource can be sure that it is
unqualified to judge the consistency of resources using properties
defined using that resource.

3.1.2 rdfs:ConstraintProperty

This resource defines a sub-class of rdf:Property, all of whose instances
are properties used to specify constraints. This class is a subclass
of rdfs:ConstraintResource and corresponds to the subset of
that class representing properties. Both rdfs:domain and
rdfs:range are instances of
rdfs:ConstraintProperty.

3.1.3 rdfs:range

An instance of ConstraintProperty that is used to constrain
property values. The value of a range property is always a
Class. The value of a property whose range is A is constrained to
be an instance of class A. A property can have at most one
range property. It is possible for it to have no range, in
which case the class of the property value is unconstrained.

Although it is not possible to express two or more range constraints on a property,
a similar outcome can be achieved by defining a common superclass for any classes
that represent appropriate values for some property. For example, to express the
constraint that a property xyz:drivesMotorVehicle can have
values which are Vans, Trucks or PassengerVehicles, we assert that
xyz:drivesMotorVehicle has a rdfs:range of
MotorVehicle. If Van, Truck and
PassengerVehicle are known to be sub-classes of
MotorVehicle, then all these types of resource are acceptable
values for
xyz:drivesMotorVehicle. In cases where a common super-class
does not exist, one can be defined in a schema in the normal manner.

As mentioned earlier, we anticipate the development of a set of classes corresponding to a
set of "datatypes." Once available, these datatypes may be used as the value of the
rdfs:range constraint property.

3.1.4 rdfs:domain

An instance of ConstraintProperty that is used to specify a
class on which a property may be used. A property may have
zero, one, or more than one class as its domain. If there is no domain
property, it may be used with any resource. If there is exactly one domain
property, it may only be used on instances of that class (which is the
value of the domain property).
If there is more than one domain property, the constrained property
can be used with instances of any of the classes (that are values of
those domain properties).

3.2 Example

Continuing with our earlier example of MotorVehicle, in this example,
we define two properties : 'registeredTo' and 'rearSeatLegRoom'.
The 'registeredTo' property is applicable to any MotorVehicle and
its value is a Person (defined in the examples below). For the sake of
this example, 'rearSeatLegRoom' only applies to Minivans and
PassengerVehicles. The value is a 'Number' (we anticipate that
some concept like this will be provided by the work on data types),
which is the number of centimetres of rear seat legroom.

4. Extensibility Mechanisms

The RDF Schema specification builds upon the foundations
provided by XML and by the RDF Model and Syntax.
It provides some additional facilities to support the
evolution both of individual RDF vocabularies, and of the core RDF Schema
specification vocabulary introduced in this document.

4.1. Evolvability of RDF vocabularies

4.1.1. Terminology

The phrase 'RDF vocabulary' is used here to refer to those resources which
evolve over time; 'RDF schema' is used to denote those resources which
constitute the particular (unchanging) versions of an RDF vocabulary at
any point in time. Thus we might talk about the evolution of the
Dublin Core vocabulary. Each version of the Dublin Core
vocabulary would be a different RDF schema, and would have a
corresponding RDF model and concrete syntactic representation.

4.1.2. Inter-Vocabulary Relationships

The resources defined in RDF schemas are themselves Web resources, and
can be be described in other RDF schemas. This principle provides the
basic mechanism for RDF vocabulary evolution. This specification does not
attempt to provide a full framework for expressing mappings between
schemas; it does however provide the rdfs:subClassOf and
rdfs:subPropertyOf properties. The ability to express
specialization relationships between classes (subClassOf) and
between properties (subPropertyOf) provides a simple
mechanism for making statements about how such resources map to
their predecessors.

There are many scenarios for which these simple mechanisms are not
adequate; a more general schema mapping mechanism for RDF may be developed
in future W3C Activity.

4.1.2.1. Examples

A schema representing version 1.0 of some vocabulary might define
classes corresponding to a number of vehicle types. The schema for version
2.0 of this vocabulary constitutes a different Web resource. If the new
schema defines for example a class 'Van' whose members are a subset of the
members of the class 'Van' in version 1.0, the
rdfs:subClassOf property can be used to state that all
instances of V2:Van are also instances of
V1:Van.

Where the vocabulary defines properties, the same approach can be taken,
using rdfs:subPropertyOf to make statements about
relationships between properties defined in successive versions of an RDF
vocabulary.

4.2. Evolvability of the RDF Schema Constraint Mechanism

This specification defines a sub-class of resources known as 'constraint
resources' (section 3.1). This is provided to allow for the addition of
new ways of expressing RDF consistency constaints.
Future extensions to the Resource Description Framework may
introduce new resources that are instances of the
rdfs:ConstraintResource class. It is
necessary to anticipate RDF content which draws upon properties or
classes defined using constraints other than those
available in this version of RDF. This specification introduces the notion
of consistent and inconsistent RDF models. As yet
unknown constraints may contribute to a more expressive
framework for specifying whether an RDF model is or is not
considered consistent.

RDF agents unfamiliar with the semantics of unknown instances of
rdfs:ConstraintResource may therefore lack the
knowledge to evaluate models for consistency when vocabulary items are
defined using those unknown constraints.
Since RDF itself may not represent declaratively the full
meaning of these constraint resources, the acquisition of RDF
statements about a new ConstraintResource may not
provide enough information to enable its use in consistency checking.
For example, when encountering a previously unknown constraint property
type called RDF3:mysteryConstraint we may learn
mechnically that it has a range of rdf:Class and a domain of
rdf:Property. The range and domain constraints if
encountered alone would be enough to tell us how to legally use
RDF3:mysteryConstraint, but they
do not tell us anything about the nature of the constraint expressed when
it is used in that fashion.

The rdfs:ConstraintResource
construct is provided here as a simple future-proofing mechanism, and
addresses some of the issues discussed at greater length in the Extensible
Web Languages W3C NOTE [EXTWEB]. By flagging new forms
of constraint as members of this class, we indicate that they are intended to express Schema
language contraints whose semantics must be understood for
consistency checking to be possible. Membership of the class
suggests, but does not imply, that those semantics may be inexpressible
in a declarative form. Since the expressive facilties available within RDF
for doing so are also likely to evolve, this distinction itself presents
a moving target. All RDF agents will have implicit knowledge of certain
constraints (for example, this specification declares that subClassOf
properties must not form a loop in an RDF graph) which may or may not be capable of
representation within (some version of) RDF. It may be the case that some future RDF
specification provides facilties which will allow RDF agents to
comprehend declarative specifications for as-yet uninvented
constraint properties. In such a case, these agents could safely
comprehend (some) previously unencountered forms of constraint. By
providing the basic rdfs:ConstraintResource class, we
anticipate such developments. All RDF agents written to this specification
will appreciate their ignorance of the meaning of unknown instances
of that class, since this specification provides no mechanism for learning
about such constraints through the interpretation of RDF statements.
Future specifications, should they offer such facilities, could also
define sub-classes of ConstraintProperty to classify new constructs
according to whether or not they had inexpressible semantics.

5. Documentation

The following properties are provided to support simple documentation
and user-interface related annotations within RDF schemas. Multilingual
documentation of schemas is supported at the syntactic level through
use of the xml:lang language tagging facility. Since RDF schemas are
expressed within the RDF data model, vocabularies defined in other namespaces may be used
to provide richer documentation.

5.1 rdfs:comment

This is used to provide a human-readable natural language description of
a resource.

5.2 rdfs:label

This is used to provide a human-readable version of a resource name.

6. Model and Syntax concepts

The RDF Model and Syntax specification [RDFMS]
introduces certain concepts. A number of these
are defined formally in another RDF Schema whose namespace URI
reference is http://www.w3.org/1999/02/22-rdf-syntax-ns#. In
addition, some further concepts are introduced in the RDF Model and Syntax
specification but do not appear in the RDF Model and Syntax
schema. These formally belong in the Schema namespace (for example,
rdfs:Literal and rdfs:Resource). In cases where
an RDF resource belongs to the http://www.w3.org/1999/02/22-rdf-syntax-ns#
namespace, this document can provide only a convenience copy of
that resource's definition.

Appendix A provides an RDF/XML schema for the RDF resources
defined in this document, including RDF Model concepts such as
Literal and Resource.
The RDF/XML Schema in Appendix A also makes RDF statements about resources
defined in the RDF Model and Syntax namespace. These have the status of
annotations rather than definitions. This is indicated
through the use of the <rdf:Description about="...">
syntax, as against the <rdf:Description ID="...">
construct used for the definitions of RDF Schema resources such as
domain and range.

6.1. rdfs:Literal

This corresponds to the set called the 'Literals' in the formal model for RDF
presented in section 5 of the Model and Syntax
specification [RDFMS]. Atomic values such as textual strings are examples of
RDF literals.

6.2. rdf:Statement

This corresponds to the set called the 'Statement' in the formal model for RDF
presented in section 5 of the Model and Syntax
specification [RDFMS].

6.3. rdf:subject

This corresponds to the property called the 'subject' in the formal model for RDF
presented in section 5 of the Model and Syntax
specification [RDFMS]. Its rdfs:domain
is rdf:Statement and rdfs:range is
rdfs:Resource. This is used to specify the resource
described by a reified statement.

6.4. rdf:predicate

This corresponds to the property called the 'predicate' in the formal model for RDF
presented in section 5 of the Model and Syntax
specification [RDFMS]. Its rdfs:domain
is rdf:Statement and rdfs:range is
rdf:Property. This is used to identify the property used
in the modelled statement.

6.5. rdf:object

This corresponds to the property called the 'object' in the formal model
for RDF presented in section 5 of the Model and Syntax
specification [RDFMS]. Its rdfs:domain is rdf:Statement.
This is used to identify the property value in the modelled statement.

6.6 rdfs:Container

This class is used to hold the Container classes described in section 3
of the Model and Syntax specification [RDFMS]. It is
an instance of rdfs:Class and rdfs:subClassOf of
rdfs:Resource.

6.7. rdf:Bag

This corresponds to the class called 'Bag' in the formal model for RDF presented
in section 5 of the Model and Syntax specification [RDFMS]. It
is an instance of rdfs:Class and
rdfs:subClassOfrdfs:Container.

6.8. rdf:Seq

This corresponds to the class called 'Sequence' in the formal model for RDF
presented in section 5 of the Model and Syntax specification [RDFMS]. It is an instance of rdfs:Class and
rdfs:subClassOfrdfs:Container.

6.9. rdf:Alt

This corresponds to the class called 'Alternative' in the formal model for RDF
presented in section 5 of the Model and Syntax
specification [RDFMS]. It is an instance of rdfs:Class and
rdfs:subClassOfrdfs:Container.

6.10. rdfs:ContainerMembershipProperty

This class has as members the properties _1, _2, _3 ... used
to indicate container membership, as described in section 3
of the Model and Syntax specification [RDFMS]. This is a
rdfs:subClassOfrdf:Property.

6.11. rdf:value

This corresponds to the 'value' property described in section 2.3
of the Model and Syntax specification [RDFMS].

7. Examples

This section gives some brief examples of using the RDF Schema
machinery to define classes and properties for some possible
applications. Note that some of these examples use the
abbreviated RDF syntax (mentioned in 2.3.2.1 above) to express class
membership.

Example 1

In this example, Person is a class with a corresponding
human-readable description of "The class of people".
A Person is a sub-class of Animal. A
Person may have an age property. The value of age is an integer. A Person may
also have an ssn ("Social Security Number") property. The value of ssn is an
integer. A Person's marital status is one of {Married, Divorced,
Single, Widowed}. This is achieved through use of the range constraint:
we define both a 'maritalStatus' property and a class 'MaritalStatus'
(adopting the convention of using lower case letters to begin the names of
properties, and capitals for classes). We then use rdfs:range to state
that a maritalStatus property only 'makes sense' when it has a value which
is an instance of the class MaritalStatus. The schema then defines a
number of instances of this class. Whether resources declared to
be of type MaritalStatus in another graph are trusted is an application
level decision.

Example 2

In this example we sketch an outline of an RDF vocabulary for
use with searchable Internet services. SearchQuery
is declared to be a class. Every SearchQuery can have both a
queryString whose value is an rdfs:Literal and a
queryService whose value is a SearchService.
A SearchService is a sub-class of InternetService (which is
defined elsewhere). A SearchQuery has some number of result
properties (whose value is SearchResult). Each SearchResult has
a title (value is a literal), a rating (value is
between 0 and 1) and of course, the page itself.

The modularity of RDF allows other vocabularies to be combined with simple
schemas such as this to characterise more fully the properties of
networked resources. For example, Dublin Core or a
library-based classification vocabulary might be used to describe the
subject coverage or collections-level properties for each SearchService,
while an independently managed "search protocols" vocabulary could
be used to describe connection details for (say) LDAP, WHOIS++ or Z39.50
search interfaces offered by the service. By allowing the
creation of statements which draw upon specialised schemas from various
domains, RDF makes it possible for communities of expertise to contribute
to a decentralised web of machine-readable vocabularies.

A. PICS-1.1 Label Vocabulary

The vocabulary that appears in a PICS-1.1 label is a mixture of descriptions
of the service providing the rating, data having to do with the mechanics
of transporting the ratings, descriptions of the ratings themselves, and
descriptions of the target resource. The vocabulary associated with the
transport mechanics (error, for) are not included here.
The generic keyword is handled by the RDF aboutURIPrefix
mechanism. Two deprecated PICS-1.1 options (signature-RSA-MD5
and MIC-MD5) are omitted from this vocabulary.

The syntax presented in the RDF/XML fragments below assumes that the RDF Model and Syntax
namespace is available using the prefix rdf:, and that the RDF Schema
namespace is the current default XML namespace.

A.1. Document Properties

The PICS 'at' option is a higher-order relation between the document
being rated and the rating statement. As such, it is modelled as a property
of the (reified) rating statement.

<rdf:Property ID="at"
comment="The last modification date of the
subject resource at the time the rating was assigned">
<domain rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Statement"/>
</rdf:Property>

A.2. Label Options

The rating service URI identifies the source of the labels. In PICS-1.1
the rating system (rating vocabulary) is identified within the service
description at the service URI. In PICS/RDF the rating vocabulary should
be identified with its own schema (and namespace name). The ratingService
property therefore serves only to identify the source of the statements.
It is an open question of semantics as to what responsibility the ratingService
has for the content of the statements.

<rdf:Property ID="ratingService"
comment="The service from whom this rating was received.">
<domain rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Statement"/>
</rdf:Property>

The remainder of the label options identify additional properties of
the rating statement itself.

<rdf:Property ID="by"
comment="An identifier for the person or entity within the rating service
who was responsible for creating this particular rating.">
<domain rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Statement"/>
</rdf:Property>
<rdf:Property ID="on"
comment="The date on which this rating was issued.">
<domain rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Statement"/>
</rdf:Property>

The PICS 'until' label option can also be written as 'exp'. We
could use subPropertyOf to represent this synonym; instead,
we eliminate it altogether in this respresentation of PICS.

A.3. Other Information

The collection of statements may have the following two properties.

<rdf:Property ID="comment"
comment="Information for humans who may see the label; no associated semantics.">
<domain
rdf:resource="http://www.w3.org/TR/1999/PR-rdf-schema-19990303#Container"/>
</rdf:Property>

The 'completeLabel' property will appear only on a container that has
not (yet) been replaced by the contents of the complete label resource.
When the complete label is used, the statements in the original collection
are withdrawn from the database and the statements in the complete label
resource are added.

<rdf:Property ID="completeLabel"
comment="A complete label that can be used in place of the current one.">
<domain
rdf:resource="http://www.w3.org/TR/1999/PR-rdf-schema-19990303#Container"/>
</rdf:Property>

B. PICS-1.1 Rating Service Description Vocabulary

A PICS Rating Service Description is essentially a schema. Some of the
vocabulary used in PICS-1.1 translates directly to the RDF Schema
vocabulary. In this RDF representation of PICS the rating system is specified separately
from the rating service, rather than as a part of the rating service.

<rdf:Property ID="ratingService"
comment="A document describing the rating service in human-readable terms."/>
<rdf:Property ID="icon"
comment="A graphic associated with the rating service or with a
specific rating property."/>

The following properties are used within the rating system schema to
describe the schema and the properties within the schema.

<rdf:Property ID="name"
comment="The name of the rating system."/>
<rdf:Property ID="description"
comment="A human-readable description of the rating system."/>
<rdf:Property ID="minimum"
comment="The minimum numeric value permitted."/>
<rdf:Property ID="maximum"
comment="The maximum numeric value permitted."/>
<Class rdf:ID="Integer"
comment="Integer numbers."/>
<Class rdf:ID="Encoding"
comment="A value with a label"/>
<Class rdf:ID="Multivalue">
<subClassOf resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/>
<!-- used as the range of properties that can take either a singleton or a Bag as their value -->
</Class>
<Class rdf:ID="Multiordered">
<subClassOf resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/>
<!-- used as the range of properties that can take either a singleton or a Seq as their value -->
</Class>

'Categories' and the transmit-as property are simply the property
name. The category name is the RDF label property.

C. Sample PICS Rating System

The "Good Clean Fun" rating system example can be written in RDF/XML as
follows:

8. Acknowledgements

Note: This document was prepared and approved for publication by the W3C
RDF Schema Working Group (WG). WG approval of this document does not necessarily
imply that all WG members voted for its approval.

David Singer of IBM is the chair of the group; we thank David for his
efforts and thank IBM for supporting him and us in this endeavor.
Particular thanks are also due to Andrew Layman for his editorial work
on earlier versions of this specification.

Not all of the people listed above have been members throughout the
entire duration of the working group, but all have contributed to the evolution
of this document.

Appendix A: XML Serialization

The RDF specification of the above is given here in the
serialization syntax. Please note that the namespace URIs listed are
examples only; formal identifiers have not yet been assigned for these
schemas. This schema includes annotations describing RDF resources defined
formally in the RDF Model and Syntax specification, as well as
definitions for new resources belonging to the RDF Schema namespace.

Note that there are some constraints (such as those given in 2.3.2
above) on certain RDF Schema resources which are themselves not fully
expressible using the RDF Schema specification. For example, the
RDF below does not tell us that subClassOf arcs should not (to use terminology from the
nodes and arcs representation) form loops in any RDF model.

Compact XML Serialization

The following is the same RDF data expressed using the more compact XML
serialisation syntax. This representation is suitable for embedding in XML
documents (such as this specification) intended for display, since the
literal string values are encoded as the values of XML attributes, and as
such are not displayed by HTML-oriented applications. The source code for
this specification contains another copy of the following XML/RDF, making
the document both human and machine readable.

Appendix B: Dublin Core

The following represents an initial schema for the simple Dublin
Core Element Set [DC]. The following schema is
for illustration purposes only; the authoritative Dublin Core Schema
will be made available by the
Dublin Core Initiative.

This schema is provided as the foundation for the Dublin Core
semantics. It is believed to be all that is needed to serve as the
foundation for future, more elaborate definitions. Future extensions
are likely to specify the structure of the values of the properties,
which will involve defining classes, the properties that apply to
those classes, and some constraints on the property values.

<?xml version='1.0'?>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:rdfs="http://www.w3.org/TR/1999/PR-rdf-schema-19990303#"
xmlns:dc="">
<rdf:Description about = "">
<dc:Title> The Dublin Core Element Set </dc:Title>
<dc:Creator> The Dublin Core Metadata Inititative </dc:Creator>
<dc:Description> The Dublin Core is a simple metadata element
set intended to facilitate discovery of electronic
resources. </dc:Description>
<dc:Date> 1995-03-01 </dc:Date>
</rdf:Description>
<rdf:Description ID="Title">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Title</rdfs:label>
<rdfs:comment>The name given to the resource, usually by the Creator
or Publisher.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Creator">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Author/Creator</rdfs:label>
<rdfs:comment>The person or organization primarily responsible for
creating the intellectual content of the resource. For example,
authors in the case of written documents, artists, photographers, or
illustrators in the case of visual resources.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Subject">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Subject</rdfs:label>
<rdfs:comment>The topic of the resource. Typically, subject will be
expressed as keywords or phrases that describe the subject or
content of the resource. The use of controlled vocabularies and
formal classification schemes is encouraged.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Description">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Description</rdfs:label>
<rdfs:comment> A textual description of the content of the resource,
including abstracts in the case of document-like objects or content
descriptions in the case of visual resources.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Publisher">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Publisher</rdfs:label>
<rdfs:comment>The entity responsible for making the resource
available in its present form, such as a publishing house, a
university department, or a corporate entity.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Contributor">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Other Contributors</rdfs:label>
<rdfs:comment>A person or organization not specified in a Creator
element who has made significant intellectual contributions to the
resource but whose contribution is secondary to any person or
organization specified in a Creator element (for example, editor,
transcriber, and illustrator).</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Date">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Date</rdfs:label>
<rdfs:comment>A date associated with the creation or availability of
the resource. Such a date is not to be confused with one belonging
in the Coverage element, which would be associated with the resource
only insofar as the intellectual content is somehow about that
date. Recommended best practice is defined in a profile of ISO 8601
[Date and Time Formats (based on ISO8601), W3C Technical Note,
http://www.w3.org/TR/NOTE-datetime] that includes (among others)
dates of the forms YYYY and YYYY-MM-DD. In this scheme, for example,
the date 1994-11-05 corresponds to November 5, 1994.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Type">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Type</rdfs:label>
<rdfs:comment>The category of the resource, such as home page,
novel, poem, working paper, technical report, essay, dictionary. For
the sake of interoperability, Type should be selected from an
enumerated list that is currently under development in the workshop
series.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Format">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Format</rdfs:label>
<rdfs:comment>The data format of the resource, used to identify the
software and possibly hardware that might be needed to display or
operate the resource. For the sake of interoperability, Format
should be selected from an enumerated list that is currently under
development in the workshop series.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Identifier">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Identifier</rdfs:label>
<rdfs:comment>A string or number used to uniquely identify the
resource. Examples for networked resources include URLs and URNs
(when implemented). Other globally-unique identifiers, such as
International Standard Book Numbers (ISBN) or other formal names are
also candidates for this element.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Source">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Source</rdfs:label>
<rdfs:comment>Information about a second resource from which the
present resource is derived. While it is generally recommended that
elements contain information about the present resource only, this
element may contain a date, creator, format, identifier, or other
metadata for the second resource when it is considered important for
discovery of the present resource; recommended best practice is to
use the Relation element instead. For example, it is possible to
use a Source date of 1603 in a description of a 1996 film adaptation
of a Shakespearean play, but it is preferred instead to use Relation
"IsBasedOn" with a reference to a separate resource whose
description contains a Date of 1603. Source is not applicable if the
present resource is in its original form.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Language">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Language</rdfs:label>
<rdfs:comment>The language of the intellectual content of the
resource. Where practical, the content of this field should coincide
with RFC 1766 [Tags for the Identification of Languages,
http://ds.internic.net/rfc/rfc1766.txt ]; examples include en, de,
es, fi, fr, ja, th, and zh.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Relation">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Relation</rdfs:label>
<rdfs:comment>An identifier of a second resource and its
relationship to the present resource. This element permits links
between related resources and resource descriptions to be
indicated. Examples include an edition of a work (IsVersionOf), a
translation of a work (IsBasedOn), a chapter of a book (IsPartOf),
and a mechanical transformation of a dataset into an image
(IsFormatOf). For the sake of interoperability, relationships should
be selected from an enumerated list that is currently under
development in the workshop series.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Coverage">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Coverage</rdfs:label>
<rdfs:comment>The spatial or temporal characteristics of the
intellectual content of the resource. Spatial coverage refers to a
physical region (e.g., celestial sector); use coordinates (e.g.,
longitude and latitude) or place names that are from a controlled
list or are fully spelled out. Temporal coverage refers to what the
resource is about rather than when it was created or made available
(the latter belonging in the Date element); use the same date/time
format (often a range) [Date and Time Formats (based on ISO8601),
W3C Technical Note, http://www.w3.org/TR/NOTE-datetime] as
recommended for the Date element or time periods that are from a
controlled list or are fully spelled out.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
<rdf:Description ID="Rights">
<rdf:type rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#Property"/>
<rdfs:label>Rights</rdfs:label>
<rdfs:comment>A rights management statement, an identifier that
links to a rights management statement, or an identifier that links
to a service providing information about rights management for the
resource.</rdfs:comment>
<rdfs:isDefinedBy rdf:resource = ""/>
</rdf:Description>
</rdf:RDF>


(library (yuni util combinators)
         (export compose)
         (import (rnrs))

;; gauche .$, compose
(define (compose . args)
  ;; from Gauche manual:
  ;; (compose f g) ==
  ;;   (lambda args
  ;;     (call-with-values
  ;;       (lambda () (apply g args))
  ;;       f))
  ;;
  ;; expanded.
  (if (pair? args)
    (let ((f (car args))
          (next (cdr args)))
      (if (pair? next)
        (let ((g (car next))
              (rest (cdr next)))
          (let ((q (lambda X
                     (call-with-values (lambda () (apply g X)) f))))
            (if (null? rest)
              q
              (apply compose (cons q rest)))))
        f))
    values))

)


Q:

How to change the color of UITabbarViewController's navigationBar?

There is a UITabBarController
- (void)getToMCGatherViewController
{
    mCGatherViewController = [[MCGatherViewController alloc] initWithNibName:@"MCGatherViewController" bundle:nil];
    UINavigationController *navigationController = [[UINavigationController alloc] initWithRootViewController:mCGatherViewController];
    navigationController.modalTransitionStyle = UIModalTransitionStyleFlipHorizontal;
    [self presentModalViewController:navigationController animated:YES];
    [navigationController release];
}

In the .h file:
 @interface MCGatherViewController : UITabBarController

In the .m file . I want to change the color of the view's navigationBar
- (void)viewDidLoad
{
    [super viewDidLoad];
    self.navigationController.navigationBar.tintColor=[UIColor greenColor];
}

and it does not work at all.
Help me with this problem , thank you in advance!

A:

just add
[navigationController.navigationBar setTintColor:[UIColor greenColor]];

after
UINavigationController *navigationController = [[UINavigationController alloc] initWithRootViewController:mCGatherViewController];

in your getToMCGatherViewController method.


Search form

Cal Women Earn Top 30 National Ranking

BERKELEY - On the strength of its fifth-place finish at last week's Pac-10 championships - the best for the program in 21 years - the Cal women's cross country team has entered the national rankings for the first time this season. The Golden Bears are rated 27th in the U.S. Track & Field and Cross Country Coaches Association's weekly poll.

In addition, Cal has moved up one spot to fifth in the West Region rankings, the Bears' highest standing of the year.

In earning its high finish at Pac-10s, Cal was led by sophomore Deborah Maier, who captured sixth individually, the highest for a Cal runner since Elissa Reidy was also sixth in 1997. Maier completed the 6000-meter course in 20:00.10 and significantly improved on her team-leading 41st-place finish as a freshman last season.


Guzmania kraenzliniana

Guzmania kraenzliniana is a plant species in the genus Guzmania. It is a member of the family Bromeliaceae. It is an epiphyte.

References

kraenzliniana
Category:Epiphytes


package build

import (
	"context"

	"github.com/werf/werf/pkg/config"
	"github.com/werf/werf/pkg/container_runtime"
	"github.com/werf/werf/pkg/storage"
	"github.com/werf/werf/pkg/storage/manager"
)

type ConveyorWithRetryWrapper struct {
	WerfConfig          *config.WerfConfig
	ImageNamesToProcess []string
	ProjectDir          string
	BaseTmpDir          string
	SshAuthSock         string
	ContainerRuntime    container_runtime.ContainerRuntime
	StorageManager      *manager.StorageManager
	StorageLockManager  storage.LockManager

	ConveyorOptions ConveyorOptions
}

func NewConveyorWithRetryWrapper(werfConfig *config.WerfConfig, imageNamesToProcess []string, projectDir, baseTmpDir, sshAuthSock string, containerRuntime container_runtime.ContainerRuntime, storageManager *manager.StorageManager, storageLockManager storage.LockManager, opts ConveyorOptions) *ConveyorWithRetryWrapper {
	return &ConveyorWithRetryWrapper{
		WerfConfig:          werfConfig,
		ImageNamesToProcess: imageNamesToProcess,
		ProjectDir:          projectDir,
		BaseTmpDir:          baseTmpDir,
		SshAuthSock:         sshAuthSock,
		ContainerRuntime:    containerRuntime,
		StorageManager:      storageManager,
		StorageLockManager:  storageLockManager,
		ConveyorOptions:     opts,
	}
}

func (wrapper *ConveyorWithRetryWrapper) Terminate() error {
	return nil
}

func (wrapper *ConveyorWithRetryWrapper) WithRetryBlock(ctx context.Context, f func(c *Conveyor) error) error {
Retry:
	newConveyor, err := NewConveyor(
		wrapper.WerfConfig,
		wrapper.ImageNamesToProcess,
		wrapper.ProjectDir,
		wrapper.BaseTmpDir,
		wrapper.SshAuthSock,
		wrapper.ContainerRuntime,
		wrapper.StorageManager,
		wrapper.StorageLockManager,
		wrapper.ConveyorOptions,
	)
	if err != nil {
		return err
	}

	if shouldRetry, err := func() (bool, error) {
		defer newConveyor.Terminate(ctx)

		if err := f(newConveyor); manager.ShouldResetStagesStorageCache(err) {
			if err := newConveyor.StorageManager.ResetStagesStorageCache(ctx); err != nil {
				return false, err
			}
			return true, nil
		} else {
			return false, err
		}
	}(); err != nil {
		return err
	} else if shouldRetry {
		goto Retry
	}
	return nil
}


864 F.2d 789
Campbellv.Sales Tax Dist. #3
NO. 87-3834
United States Court of Appeals,Fifth Circuit.
DEC 19, 1988
Appeal From:  E.D.La., 673 F.Supp. 790

1
AFFIRMED.


Perhaps most notably, the new space will host the third class of Google's Launchpad Accelerator, a part of the company meant to give startups resources and up to $50,000 in equity-free funding. Previous classes the Launchpad Accelerator came from Brazil, Indonesia, Mexico and India, and Google's blog post announcing its new space notes that it wants to use it to help bridge Silicon Valley with startups from emerging markets around the world. It's been less than a year since the Launchpad Accelerator started, but it seems that Google's keen to keep investing in its program.

Other details on what Google intends to do with this huge space aren't available yet, and the company hasn't said yet when it'll open -- but Google says it'll have more details in the coming weeks.


Interleukin 6/gp130-dependent pathways are protective during chronic liver diseases.
The contribution of the acute phase inducer interleukin 6 (IL-6) in the pathogenesis of liver diseases is yet unclear. Our analysis showed enhanced expression of IL-6 in livers derived from patients with acute and chronic liver diseases. Additionally, IL-6 plasma levels were significantly increased in patients with chronic liver diseases and showed an inverse correlation with biochemical markers of liver function and a positive correlation with inflammatory markers, signs of portal hypertension, and the degree of liver fibrosis. To prove the relevance of these clinical findings, we applied the tetrachlorcarbonide (CCl(4)) model to conditional knockout animals (Cre/loxP system) for gp130, the common signal transducer of IL-6 family cytokines. Cre recombinases were expressed through a hepatocyte (AlfpCre) and a ubiquitous (MxCre) control element. Gp130 deleted mice had a totally abolished STAT3 activation and acute phase response induction, but gp130 deletion had no effect on the degree of acute liver injury and subsequent hepatocyte proliferation. In contrast, during chronic liver injury induced by biweekly application of CCl(4), deletion of the gp130 receptor in nonparenchymal liver cells and not hepatocytes resulted in fibrosis progression. In conclusion, our experiments indicate an involvement of IL-6 in the pathogenesis of liver diseases and suggest a protective role of IL-6/gp130-dependent pathways in nonparenchymal liver cells during fibrosis progression in chronic liver diseases. (Hepatology 2003;38:218-229).


Q:

Accessing Celery instance outside of Virtualenv

I have a flask based API operating inside of a virtual environment on my server.  I wish for my API to call celery tasks however Celery is installed and already running for other purposes outside of the virtual environment that the API runs in.  How do I import my tasks module in such a way that it can be used inside of the virtualenv.
Sorry if this is a dumb question using Virtualenv is new to me.

A:

You just have to install the dependencies required to load the 'tasks' module inside the virtualenv too (e.g. pip install celery).
The act of sending the task is not really related to the virtualenv, it only needs to communicate with the right broker URL (this can be a bit more complicated when using e.g. the Django database as a broker though).
In fact you easily send a task by name too:
$ python
>>> from celery import Celery
>>> Celery(broker='amqp://').send_task('tasks.add', (2, 2))

So the broker is the only required communication point, but the tasks.py module and Celery application can contain configuration that affect how tasks are sent (like routing to different queues, setting default queue names and queue + task configuration and so on).


Nick Gravante of Boies Schiller Flexner

For Nick Gravante and Natasha Harrison, managing partners at Boies Schiller Flexner, the decision to keep the firm’s summer associate program was a quick one. They said Wednesday that after the issue was raised internally, the firm’s leaders mailed its roughly 28 summer associates a letter assuring them that the program would go on.

Natasha Harrison of Boies Schiller Flexner

A goal of the summer program is to give rising lawyers “a real dose of reality,” Gravante said, and for now that includes dealing with a pandemic. “If we have to work at home because that’s where lawyers are working when summer associates start arriving in mid-May, then we will incorporate the summers into our work-from-home routine.”

But many other law firms still seem to be trying to work out the kinks. While lateral hiring has continued at many firms, summer associate programs are traditionally centered around face-to-face interaction and forging links with future colleagues. It will doubtlessly be more challenging to do that over video chats and emails.

At Paul, Weiss, Rifkind, Wharton & Garrison, chairman Brad Karp said Thursday that the firm still hadn’t decided whether to change its summer associate program. But he noted that delaying summer associate programs beyond their usual mid-May starting point could dovetail with the decision by most law schools to delay their on-campus interviews from about August 2020 until early 2021, freeing up students later in the summer.

Nathan Peart, a managing director at recruiting firm Major, Lindsey & Africa’s associate practice group, said decisions about changes to the summer associate program were still up in the air at many firms, but they generally view it as a key part of their talent pipeline. He said in a Thursday interview that he hadn’t yet heard of any firms that planned to cancel or shorten their summer programs.

“In the next two weeks, I think that’s when we’ll get more clarity on these things,” he said.

Other firms that have said in recent weeks they plan to go ahead with their summer programs include Fried, Frank, Harris, Shriver & Jacobson and Caplin & Drysdale.

A spokesman for Covington & Burling also said in an email Thursday that the firm plans to move forward with its summer program as planned, even if participants need to start remotely.

Joel Carpenter, the Boston-based managing partner of Sullivan & Worcester, said Wednesday that switching to remote work has gone well. But with the economy entering a sharp downturn, he said, his firm has made some cuts—cancelling a partner retreat later this year—and is figuring out what to do in other areas. He said the firm hasn’t decided whether it will make any changes to its four-person summer associate program.

“You see [the economic forecasts], and you say, ‘how can that not affect me?’” he said.

At Boies Schiller, Harrison said, while not everyone could work at 100% productivity under the current conditions, they are still chugging along. Harrison, who started the firm’s London office, said English courts have been highly adept at moving arguments to the videoconferencing product Zoom, and even happy hours have gone digital.

“We had our first drinks-from-home on Friday, where everyone dials in on Zoom,” she said.


Paul Nuttall: We must join other countries in banning the Muslim Brotherhood There are times in politics, as in life, that it is great to be vindicated. Last year’s Referendum result was […]

There are times in politics, as in life, that it is great to be vindicated. Last year’s Referendum result was one of those times, where the nation voted clearly to leave the European Union, a position that I and Ukip had been laughed at and derided for only a couple of years earlier.

‘We are pleased the other parties have started to follow our lead, but appalled that it has taken such horrific events to make it happen’

But there are other times that you wish you were wrong. In the aftermath of the Westminster, Manchester and London Bridge attacks what we have been saying about cutting out the cancer of Islamist terror in our midst has been shown to have been horrifically correct.

i's opinion newsletter: talking points from today Email address is invalid Email address is invalid Thank you for subscribing! Sorry, there was a problem with your subscription.

For too long, our leaders of all stripes have hidden the truth from the people of this country about the source of this campaign against us and our values, and only now we are hearing a few words of admission.

We need action, not words

But they are still only words. And we need action to protect us, not more words.

There are things we can do as a nation to protect ourselves from these fanatics, but it demands greater will than we see in either the Tories or Labour.

We need to bar anybody who has gone to Syria or elsewhere to take up arms on behalf of Islamic State from returning.

We need to deport foreign nationals back to their home countries if they are known to subscribe to the tenets of Islamist terror.

We need to close down mosques which encourage Islamist teaching of hate against us and our society.

We need to stop Saudi and Qatari funding of Mosques and Islamist institutes.

We need to reverse the Tory cuts in police numbers and bring 20,000 police back.

We need to consider far greater routine armed police.

We need to support our intelligence services with greater resources and beef up our border guards.

And we need to scrap the Human Rights Act and replace it with a British Bill of Rights.

All this was Ukip policy before the attacks, and remains so now.

In addition, we need to proscribe the Muslim Brotherhood, as many countries already have. This is an organisation that promotes hatred and intolerance both at home and abroad.

We are pleased the other parties have started to follow our lead, but appalled that it has taken such horrific events to make it happen. Ukip leads the agenda, and its only by voting for Ukip where we are standing that the agenda will continue to be set.


Current therapeutic approaches to rheumatoid arthritis (RA) (corticosteroids, methotrexate, neutralization of TNF-?) rely upon broad-spectrum immunosuppression, an approach that is not uniformly effective and is frequently associated with significant side-effects. To address this market gap, Radikal Therapeutics (RTX) is developing a novel soluble receptor decoy receptor fusion protein (hR-421) that induces immune tolerance in antigen (Ag)-specific activated T-cells. Constructed from Ig-Fc and the second ecto domain of the CCR5 receptor, hR-421 binds and neutralizes al 3 CCR5-binding chemokine ligands (MIP-?, MIP-?, RANTES) and prevents their binding and activation of the CCR1, CCR3, and CCR5 membrane receptors. In contrast to CCR5 inhibitors, mR-421 (the murine homologue of hR-421) blocks CCR5-independent pro-inflammatory pathways and is effective in CCR5 knock-out mice. Therapy with mR- 421 profoundly suppresses experimental allergic encephalomyelitis (EAE), a classic autoimmune model system, even when treatment is initiated after disease onset. Moreover, Ag-specific effector Th1 cells isolated from EAE donors treated in vivo with mR-421 produce substantially less pro-inflammatory cytokines and suppress EAE in adoptive transfer experiments. This latter effect is driven by the ability of mR-421 to prevent the co-stimulatory signal on Th1 CD4+ T cells. Based on these findings, we hypothesize that R-421 will prevent co-stimulation and thus the downstream proliferation and activation of Th1 CD4+ cells in RA. We now propose to extend the protective effects of the R-421 technology beyond the published findings in neuroinflammation and establish its potential benefit in a clinically-relevant model of RA. Male DBA mice inoculated with collagen in CFA and rechallenged on Day 21 to induce autoimmune arthritis, will be treated with mR-421 (2, 4, 8 mg/kg), an irrelevant IgG1 control, or etanercept (6.25 mg/kg) beginning at the time of significant disease (Day 21), as characterized by an arthritic score of 2 (scale of 0-16). Additionally, we will include a sham control group not exposed to collagen/CFA or treatment. Animals will be monitored for clinical evidence of arthritis over a period of 6 weeks, a timepoint characterized in controls by erythema and edema of the entire paw including digits (score=12). Plasma m-R421 concentrations will be related to clinical outcome, so as to construct a pharmacodynamic profile that will guide future clinical dosing. We expect mR-421 to reduce joint injury, in a dose and plasma concentration dependent fashion, as defined by a reduction in the mean arthritic score that is equivalent or superior to the treatment effect elicited by the gold-standard clinically-approved agent etanercept. These findings are expected to parallel the effects of mR-421 on synovial lipid peroxidation, neutrophil infiltration, pro-inflammatory gene expression peroxynitrite production, poly(ADP-ribose)polymerase formation, and gross and histologic injury scores, and on draining lymph node populations of Th1 and Treg lymphocytes. PUBLIC HEALTH RELEVANCE: Rheumatoid arthritis is a devastating autoimmune disease characterized by lifelong disability and inexorable progression. Currently approved agents are partially effective and nearly one-third of patients do not obtain adequate relief. We are developing a novel drug that specifically blocks the specific immune disturbance that underlies this condition. We will test this agent in a clinically-relevant small animal model and determine the most effective dose, in anticipation of definitive large animal studies to confirm its efficacy and safety.


 3*n + 1. Let k(m) = -9*m**3 - 9*m**2 + 5*m + 1. Give x*r(i) + 3*k(i).
-2*i**3 - 2*i**2 - 2
Let t(j) = 10*j - 91. Let y(v) = 2*v + 3. Give t(o) - 4*y(o).
2*o - 103
Let k(j) = 9*j - 10. Let i(p) = -p**2 - 6*p + 12. Let c be i(-7). Suppose -s - 2*h + 4 = 0, 2*h + 21 = c*s - 11. Let w(m) = 4*m - 5. Calculate s*k(y) - 13*w(y).
2*y + 5
Let i(k) = -4*k**2 - 3*k + 2. Let y(q) = 2*q**2 + 3*q - 3. Give 3*i(g) + 2*y(g).
-8*g**2 - 3*g
Let l(g) be the first derivative of 14*g**3/3 + 17*g**2/2 + 4*g + 78. Let u(c) = -5*c**2 - 6*c - 1. Calculate -4*l(a) - 11*u(a).
-a**2 - 2*a - 5
Let g(a) = 30*a**3 + 22*a**2 + 74*a - 8. Let c(w) = 20*w**3 + 14*w**2 + 49*w - 5. Calculate -8*c(q) + 5*g(q).
-10*q**3 - 2*q**2 - 22*q
Let c(p) = -p**2 - 2*p + 3. Let b(k) = k**3 + 18*k**2 - 2*k - 34. Let o be b(-18). Let u(q) = -315*q**2 + 16 + 310*q**o + 0*q - 11*q. Give 11*c(t) - 2*u(t).
-t**2 + 1
Suppose 5*i - i + 7 = 5*s, -12 = 3*i + 3*s. Let h(o) = -3. Let g(a) be the first derivative of a**2/2 + 2*a - 7. Give i*g(c) - 2*h(c).
-3*c
Let i(w) = -11*w - 69. Let f(x) = -5*x - 35. Determine -13*f(d) + 6*i(d).
-d + 41
Let s(h) = 8*h**3 - 9*h**2 + 9*h - 10. Suppose -87 = -9*r + 75. Let k(l) = l**3 - l**2 + l - 1. Determine r*k(j) - 2*s(j).
2*j**3 + 2
Let x(g) = -4*g + 2. Let m(h) = -21*h + 11. Let v = -305 + 303. Let k(z) = -11*z. Let f be k(-1). Determine f*x(l) + v*m(l).
-2*l
Let o(y) = 159*y**2 - 26*y. Let q(f) = 32*f**2 - 5*f. Calculate 2*o(d) - 11*q(d).
-34*d**2 + 3*d
Let k(f) = -f**2 - 2*f + 2. Let o(b) = 896*b**2 + 1344*b - 1344. What is -672*k(s) - o(s)?
-224*s**2
Let q(v) = -2*v**3 + 6*v**2 - 11*v. Let h(p) = -2*p**3 + 5*p**2 - 11*p. What is -5*h(n) + 4*q(n)?
2*n**3 - n**2 + 11*n
Let i(v) = 8*v**3 - 4*v**2 + 6*v - 6. Let t(y) = y + 4*y**2 - 3*y - 3*y + 0 - 5*y**3 + 5 - 2*y**3. Calculate 5*i(u) + 6*t(u).
-2*u**3 + 4*u**2
Let s(t) = -4*t + 9. Suppose -15 = -b - 3*q, q = b + 4*b - 11. Let o(j) be the first derivative of -b - 2*j + 4*j + 4*j - j**2 - 2*j. What is -5*o(v) + 2*s(v)?
2*v - 2
Let d(a) = 413*a + 3. Let h(s) = s + 1. Determine -2*d(m) + 6*h(m).
-820*m
Let f(n) = -n. Let a(x) be the second derivative of x**4/12 - 7*x**3/6 - 5*x**2/2 + 18*x. Let u(g) = 1. Let o(h) = a(h) + 5*u(h). What is -6*f(c) + o(c)?
c**2 - c
Let d(b) = -14*b - 23. Let g(v) = 42*v + 69. Let x(s) = -11*d(s) - 4*g(s). Let k = 48 - 42. Let j(h) = 5*h + 8. Calculate k*x(r) + 17*j(r).
r - 2
Let i be 31/(-5) - 4/5. Let u = 12 + i. Suppose 4*t + 21 - u = 0. Let k(b) = -2*b**3 - 4*b**2. Let g(f) = 4*f**3 + 9*f**2. What is t*g(v) - 9*k(v)?
2*v**3
Let c(x) = 2*x - 3. Let t(k) = -48*k + 9. Let u(o) = 89*o - 18. Let l(d) = -11*t(d) - 6*u(d). Calculate 8*c(v) + 3*l(v).
-2*v + 3
Let t(a) = -2*a**2 - 3*a - 3. Let s(j) be the first derivative of -6*j**3 - 13*j**2 - 26*j - 48. What is 6*s(h) - 52*t(h)?
-4*h**2
Let j(o) = -331*o**2 + 2*o + 2. Let x(l) = 489881*l**2 - 2961*l - 2961. Calculate -2961*j(t) - 2*x(t).
329*t**2
Let k(z) = 1. Let h(l) be the second derivative of l**4/24 - 9*l**2/2 - 20*l. Let x(p) be the first derivative of h(p). Calculate -2*k(a) + x(a).
a - 2
Let t(c) = -474*c - 21. Let l(p) = -711*p - 29. What is 5*l(y) - 7*t(y)?
-237*y + 2
Let n(q) = 3*q**3 + 4*q + 6. Let x = -711 + 700. Let g be ((-2)/(-4))/((-2)/(-32)). Let y(b) = b**2 - g*b**3 - b**2 - 17 - 11*b. Determine x*n(w) - 4*y(w).
-w**3 + 2
Let l(z) = -13*z + 6. Suppose 0 = -4*j - 2 - 22. Let m(p) = -p + 1. Give j*m(y) + l(y).
-7*y
Let a(i) = 39*i**3 - 7*i**2 - 12. Let v(p) = 13*p**3 - 2*p**2 - 4. Give 2*a(r) - 7*v(r).
-13*r**3 + 4
Let h(k) = 6*k**2 + 2*k + 3. Let q(b) = 2. What is h(n) - 3*q(n)?
6*n**2 + 2*n - 3
Let t(u) = 0*u + 6*u + 1 - 8*u. Let a(k) = 1. Suppose -4*c = -0 - 8, -5*o = -c - 8. Give o*a(y) - t(y).
2*y + 1
Let d(k) = -k**3 - 431*k**2 - k. Let u(s) = -2*s**3 - 863*s**2 - 2*s. Determine -13*d(m) + 6*u(m).
m**3 + 425*m**2 + m
Let u(p) = -p + 1. Let k be (-148)/(-16) + 18/24. Suppose 5*z + 25 = k*z. Let c(m) = -7*m + 4. Give z*u(n) - c(n).
2*n + 1
Let x(m) = -2*m**3 - m**2 + 1. Let n(w) = 3*w**3 + 3*w**2 - 340. Calculate -n(p) - 3*x(p).
3*p**3 + 337
Suppose 0 = -31*n + 74*n - 32*n - 22. Let t(r) = -3*r + 2. Let w(u) be the second derivative of -7*u**3/6 + 5*u**2/2 + u. What is n*w(j) - 5*t(j)?
j
Let n(g) = 4*g**3 + 5*g - 15. Let h(z) = z**3 + z - 3. Let a(k) = -5*h(k) + n(k). Let b(m) = -m. Calculate 2*a(c) - b(c).
-2*c**3 + c
Let w(u) be the first derivative of -u**4/12 - u**3/3 - 20*u - 2. Let i(z) be the first derivative of w(z). Let k(c) = -c**2 - 5*c. Determine -5*i(b) + 2*k(b).
3*b**2
Let w(g) = -2*g**2 - g - 4. Let a = -2 - -7. Let m(r) be the second derivative of 1/6*r**4 + 0 + 12*r + 5/2*r**2 + 1/6*r**3. Determine a*w(t) + 4*m(t).
-2*t**2 - t
Let w(c) = c**3 + 2*c**2 + c. Let m(v) = -5*v**3 - 12*v**2 - 6*v + 111. Calculate -m(o) - 6*w(o).
-o**3 - 111
Suppose s - 5*m = 4 - 26, -s + 2*m - 19 = 0. Let f(y) = -41*y + 17. Let u(h) = 14*h - 6. Determine s*u(r) - 6*f(r).
8*r
Let r(z) = 3*z - 21. Let b(j) be the second derivative of -j**3/6 + 5*j**2/2 - 5*j - 7. What is 9*b(d) + 2*r(d)?
-3*d + 3
Let i(p) = 11*p + 107. Let v(s) = 19*s + 215. Give 7*i(f) - 4*v(f).
f - 111
Let i(t) = 287*t**3 - 56*t**2 - 28. Let z(f) = -f**3 + 2*f**2 + 1. Calculate i(g) + 28*z(g).
259*g**3
Let w(u) = -606*u + 1. Let v(p) = -1820*p + 3. Determine 3*v(l) - 8*w(l).
-612*l + 1
Let f(w) = -22*w - 257. Let u(z) = 10*z + 129. Calculate -4*f(r) - 9*u(r).
-2*r - 133
Let k(u) = -u**3 + 11*u**2 - 3*u - 1. Let h(q) = -2*q**2 + q - 3. What is -4*h(i) - k(i)?
i**3 - 3*i**2 - i + 13
Let j(h) = 703*h + 4. Let z(u) = -712*u - 5. Determine -3*j(r) - 2*z(r).
-685*r - 2
Let q(b) = 9*b - 4. Let g(d) = 19*d + 33*d - 9*d + 70*d - 14*d - 45. Determine -4*g(u) + 45*q(u).
9*u
Let j(l) = 1159*l - 7. Let c(b) = -586*b + 4. Determine 10*c(o) + 6*j(o).
1094*o - 2
Let u(v) be the first derivative of v**4/4 + v**3/6 - 5*v**2 - 20. Let g(a) be the second derivative of u(a). Let n(c) = 2*c. Determine 4*g(j) - 11*n(j).
2*j + 4
Let m(u) = 47*u + 1. Let z(i) = 234*i + 5. What is -11*m(n) + 2*z(n)?
-49*n - 1
Let v(o) = -2*o**2. Let z(p) = 5*p**2 + 3. Let c(r) = -9*r**2 - 5. Let f(x) = 3*c(x) + 5*z(x). What is -3*f(l) + 2*v(l)?
2*l**2
Let p(d) = -3*d**2 - 6*d + 6. Let t(w) = 2*w**2 + 5*w - 5. Let z be 6/((-9)/(-30)*5). Let a = z + -1. Determine a*p(s) + 4*t(s).
-s**2 + 2*s - 2
Suppose -3*w + 4*q - 10 = -5*w, -3*w - 2*q = -19. Let x(g) = 9*g - 9. Let a(n) = -8*n + 8. Let z(k) = 0 - k - 1 - 1 + 5*k. Let b be z(2). Give b*x(d) + w*a(d).
-2*d + 2
Let n(f) be the third derivative of -f**4/24 - f**3/2 - 76*f**2. Let u(v) = -v + 1. Determine n(g) + 3*u(g).
-4*g
Suppose 0 = -f, -5*v = -3*v + f - 4. Let d = -13 - -2. Let j(o) be the first derivative of 5*o**2 + 11*o - 6. Let g(b) = 2*b + 2. Determine d*g(x) + v*j(x).
-2*x
Let p(s) = 9*s**3 - 10*s**2 - s - 12. Let t(o) = -8*o**3 + 8*o**2 + 11. Give -4*p(r) - 5*t(r).
4*r**3 + 4*r - 7
Let k(b) = -26*b + 614. Let s(i) = 31*i - 614. Calculate 6*k(a) + 5*s(a).
-a + 614
Let f(j) = 16*j**3 + 11*j**2 - 6. Let q(a) = 2 + 124*a**2 + 3*a**3 - 15 + 6 - 122*a**2 + 6. Let s be (-5)/15 - 67/(-3). What is s*q(b) - 4*f(b)?
2*b**3 + 2
Suppose -12*j + 33 = -11*j. Let r = -38 + j. Let k(h) = -10*h - 5. Let q(c) = -7*c - 3. What is r*k(o) + 7*q(o)?
o + 4
Let g(v) = 16*v**2 - 13*v - 8. Let s(b) = 12*b**2 - 11*b - 7. Calculate 4*g(h) - 5*s(h).
4*h**2 + 3*h + 3
Let h(o) = -463*o**3 - 6*o**2 - 6*o. Let g(u) = -4170*u**3 - 55*u**2 - 55*u. Give -6*g(v) + 55*h(v).
-445*v**3
Let s(v) = 85*v**3 + 25*v**2 + 25*v - 25. Let t = 144 + -142. Let n(i) = 2*i**2 + t*i + 1 + 0 + 7*i**3 - 3. Calculate -25*n(j) + 2*s(j).
-5*j**3
Let l(i) = -6*i + 256. Let q(n) = 11*n - 510. Give -5*l(j) - 3*q(j).
-3*j + 250
Let b(s) = 711*s**3 - 11*s**2 + 33*s. Let q(j) = 178*j**3 - 3*j**2 + 9*j. Calculate 6*b(u) - 22*q(u).
350*u**3
Let b(y) = -2*y**2 - 5*y - 35. Let n(s) = 2*s**2 + 4*s + 35. What is 2*b(z) + 3*n(z)?
2*z**2 + 2*z + 35
Let s(q) = -1. Let w(l) = 4 + 10*l - 9*l - 7*l + l. Let m be ((-5)/10)/(1/2). Determine m*w(u) - 3*s(u).
5*u - 1
Suppose 0 = -0*n + 3*n - 6. Let j(l) = -5*l + 0 - 3 - n*l**2 + 5. Let o(p) = 2*p**2 + 6*p - 2. What is -5*j(r) - 4*o(r)?
2*r**2 + r - 2
Let f(n) = 117*n**3 - 6*n**2 + n - 4. Let k(h) = 233*h**3 - 11*h**2 + 2*h - 7. What is 7*f(c) - 4*k(c)?
-113*c**3 + 2*c*


For most of history, next to no measurable growth in output per person
occurred. What growth did occur came from rising population.

This is not the case. Per capita economic growth was significant and economically transformative prior to 1750, according to the research cited by Gordon for the United Kingdom (PDF).

Far more importantly than what happened before 1750, Wolf republishes Gordon's "stair step decline" graph which shows rates of per capita GDP growth dropping from about 2.5% per year in 1950 to about half that a half-century later. As I have shown from multiple datasets, that trend is not supported by the data.

A linear trend on rates of change in per capita GDP from 1950 to 2006 shows very little deviation from a 2.0% growth rate, as indicated in the graph above.

How might one fool oneself into thinking otherwise?

Consider the graph above which shows change in per capita growth rates for each decade from 1885 (that is, the first point shows per capita GDP growth from 1885-1895, the second point 1895-1905, etc, based on Maddison data cited by Gordon). The data might arguably be used to support a claim of a slowdown in growth rates since 1950.

But hold on a second. Consider the graph immediately above which shows the same Maddison data, except the data begins in 1880 (i.e., the first point shows the growth rate in per capita GDP 1880-1890, the second point 1890-1900). This way of analyzing the data shows what seems to be an increase in per capita GDP growth rates from mid-century.

Which is correct? Well, they both are "correct" from a mathematical perspective. From an economic perspective, what the two graphs tell you is that the data is noisy and start and end points for analysis make a big difference. The different pictures also offer a warning about the perils of taking trends off of smoothed data.

Above is all of the data at annual resolution from 1870 to 2006. The data show a remarkable lack of trend (red line) over 136 years. There is a notable change in variability following World War II which presumably reflects the impacts of explicit monetary policies.

But over the long term, is there evidence of a great slowdown in rates of per capita economic growth? The answer is no.

Martin Wolf has promised me that he'd take a look at the data himself, which I appreciate. As the motto of Royal Society says, nullius in verba. Mistakes can easily occur in any analysis. The important thing is what is done once they are recognized.


Property Description

Beautiful remodeled home in the heart of the Arbors at Lake Crest. Walk in to a spacious foyer & 9 ft ceiling on main. Living room has gas fireplace with marble surrounding. Separate dining room. Large remodeled kitchen with lots of beautiful cabinets, granite counter tops, breakfast bar, granite table and bench to remain, & stainless appliances. Laundry room off the kitchen with mud room. Beautiful remodeled half bath on main. Large coat closet that is great for extra storage. Bamboo hardwood floors throughout main floor. Hardwood stairs going to upper level. Upstairs has a large master suite with bonus sit area/office and master bath with separate double shower, jetted tub, Double vanity, large walk-in closet. New hardwood floors in master and hallway. 3 other spacious bedrooms upstairs, each with a walk-in closet. Full bath. Large level backyard with patio area & privacy fence. New Dimensional Roof. Community pool, club house & playground, convenient to shops, grocery stores & 459.