A knowledge-based system under uncertainties and/or incompleteness, referred to as augmented knowledge base (AKB) is provided, including constructing, reasoning, analyzing and applying AKBs by creating objects in the form E→A, where A is a rule in a knowledgebase and E is a set of evidences that supports the rule A. A reasoning scheme under uncertainties and/or incompleteness is provided as augmented reasoning (AR).
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for at least one computer to represent a knowledge base, comprising: at least one memory that stores a mapping of values to sets of evidences U in the knowledge base; executing by the at least one computer: creating objects in form E→A for the knowledge base, where A is a rule among rules in the knowledge base, and E is a subset of the sets of evidences U from the knowledge base that supports the rule A, so that the rule A is supportable by the set of evidences E; determining relationship constraints κ in form of set relations among a plurality of sets of evidences E; and computing for a target rule L, a first composite object ω1→G1→L0, the first composite object ω1 constructed from a combination of the objects E→A to create a composite sets of evidences G1 subject to the relationship constraints κ which support a composite rule L0, the composite rule L0 being a combination of the rules implying the target rule L according to deductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1 indicative according to the deductive reasoning of a first validity and/or a first plausibility value for the target rule L. 2. The method according to claim 1, wherein: the mapping of the values to the sets of evidences U is according to at least one measurement function, the at least one measurement function indicative of a strength of the first validity and/or the first plausibility value for the target rule L, the computing the first composite object ω1 includes computing the first validity and/or the first plausibility value by determining a value of the G1 using the mapped values of the plurality of sets of evidences E, thereby the first validity and/or the first plausibility value indicative of the strength of validity and/or plausibility for the target rule L according to the measurement function. 3. The method according to claim 2, wherein the at least one computer further executes: extending a measurement function from among the at least one measurement functions by: selecting the measurement function which is probabilistic to filter anomalies associated with the composite rule L0 implying the target rule L; representing the relationship constraints Cκ using directed and/or undirected graphs; insuring that the directed and/or undirected graph representations of the relationship of constraints κ is admissible and compatible with the measurement function; processing the measurement function subject to the relationship constraints Cκ to obtain a new measurement function free of any relationship constraints; and applying the new measurement function to map new values to the sets of evidences E. 4. The method according to claim 1, wherein the relationship constraints Cκ include one or any combination of a subset type relation or a disjoint type relation among the plurality of sets of evidences E. 5. The method according to claim 1, wherein the at least one computer further executes: creating a largest composite sets of evidences G according to a union of a plurality of composite sets of evidences G1, subject to the relationship constraints Cκ, which support the composite rule L0; and computing a composite object ωv2 indicative of a second validity value for target rule L. 6. The method according to claim 5, wherein the computer further executes: obtaining a set complement of the largest composite sets of evidences G that supports negation of the target rule L; and computing a composite object ωp2 indicative of a second plausibility value for the target rule L. 7. The method according to claim 5, wherein: the computer further executes adding a new object in form U→L′, where the new object is a negated target rule L′ supported by the U, to the knowledge base, to thereby provide an expanded knowledgebase; and the largest composite sets of evidences G is created from the expanded knowledgebase that supports a logical falsehood F created on basis of the negated target rule L′, subject to the relationship constraints κ which support the composite rule L0, to thereby compute the second validity value for the target rule L. 8. The method according to claim 6, wherein: the at least one computer further executes adding a new object in form U→L, where the new object is the target rule L supported by the U, to the knowledge base, to thereby provide an expanded knowledge base; and the largest composite sets of evidences G is created from the expanded knowledge base that supports a logical truth T created on basis of the target rule L, subject to the relationship constraints κ which support the composite rule L0; to thereby compute the second plausibility value for the target rule L. 9. The method according to claim 1, wherein the rule A is uncertain and/or incomplete based upon the E being the subset of the sets of evidences U, thereby the computed first composite object ω1 being indicative of the first validity and/or the first plausibility value for the target rule L according to the uncertain and/or incomplete rule A supported by the subset E. 10. The method according to claim 1, wherein the at least one computer further executes: determining a complement of the first composite object ω1′=G′1→L′0, the complement of the first composite object ω1′=G′1→L′0 being a complement of the composite sets of evidences G′ and a negation of the composite rule L0′, subject to the relationship constraints κ; and computing for the target rule L, a second composite object ω2=G2→L0, the second computed composite object ω2 being indicative by inductive reasoning of a third validity and/or a third plausibility value for the target rule L. 11. The method according to claim 5, wherein the creating the largest composite sets of evidences G comprises: repeatedly combining two or more sets of evidences E of a composite sets of evidences G1 by merging rules A and taking intersection of corresponding sets of evidences E, subject to the relationship constraints κ among the sets of evidences E. 12. The method according to claim 1, wherein the at least one computer further executes: constructing a higher order knowledge base according to different methods of removing and/or altering objects E→A in the knowledge base that are inconsistent with other objects E→A, wherein the creating the objects in the form E→A is for the higher order knowledge base. 13. The method according to claim 1, wherein the knowledgebase is a Free-Form Data Base generated according to a conversion of relational data bases and/or deductive data bases to the Free-Form Database. 14. The method according to claim 10, wherein the knowledgebase is a Free-Form Data Base generated according to a conversion of relational data bases and/or deductive data bases to the Free-Form Database. 15. The method according to claim 4, wherein the relationship constraints κ are input. 16. At least one server, comprising: a non-transitory computer readable storage medium configured to store: a mapping of values to sets of evidences U in a knowledge base, and objects in the form E→A, where A is a rule among rules in the knowledge base, and E is a subset of the sets of evidences U from the knowledge base that supports the rule A, so that the rule A is supportable by the set of evidences E; and a processor coupled to the at least one memory and configured by instructions, which when executed by the processor, cause the processor to execute: determining relationship constraints κ in form of set relations among a plurality of sets of evidences E; and computing for a target rule L, a first composite object ω1−G1→L0, the first composite object ω1 constructed from a combination of the objects E→A to create a composite sets of evidences G1 subject to the relationship constraints κ which support a composite rule L0, the composite rule L0, the composite rule L0 being a combination of the rules implying the target rule L according to deductive reasoning indicated by the mapping of the values to the sets of evidences U, the first composite object ω1 indicative according to the deductive reasoning of a first validity and/or a first plausibility value for the target rule L. 17. The at least one server according to claim 16, wherein: the mapping of the values to the sets of evidences U is according to at least one measurement function, the at least one measurement function indicative of a strength of the first validity and/or the first plausibility value for the target rule L, and the computing the first composite object ω1 includes computing the first validity and/or the first plausibility value by determining a value of the G1 using the mapped values of the plurality of sets of evidences E, thereby the first validity and/or the first plausibility value indicative of the strength of validity and/or plausibility for the target rule L according to the measurement function. 18. The at least one server according claim 17, wherein the processor further executes: extending a measurement function from among the at least one measurement functions by: selecting the measurement function which is probabilistic to filter anomalies associated with the composite rule L0 implying the target rule L; representing the relationship constraints κ using directed and/or undirected graphs; insuring that the directed and/or undirected graph representations of the relationship of constraints κ is admissible and compatible with the measurement function; processing the measurement function subject to the relationship constraints κ to obtain a new measurement function free of any relationship constraints; and applying the new measurement function to map new values to the sets of evidences E. 19. The at least one server according to claim 16, wherein the relationship constraints κ include one or any combination of a subset type relation or a disjoint type relation among the plurality of sets of evidences E. 20. The at least one server according to claim 16, wherein the processor further executes: determining a complement of the first composite object ω1′=G′1→L′0, the complement of the first composite object ω1′=G′1→L′0 being a complement of the composite sets of evidences G′ and a negation of the composite rule L0′, subject to the relationship constraints κ; and computing for the target rule L, a second composite object ω2=G2→L0, the second computed composite object ω2 being indicative by inductive reasoning of a second validity and/or a second plausibility value for the target rule L. 21. The at least one server according to claim 16, wherein the processor further executes: creating a largest composite sets of evidences G according to a union of a plurality of composite sets of evidences G1, subject to the relationship constraints κ, which support the composite rule L0; and computing a composite object ωp2 indicative by deductive reasoning of a second validity value for target rule L. 22. The at least one server according to claim 21, wherein the processor further executes: obtaining a set complement of the largest composite sets of evidences G that supports negation of the target rule L; and computing a composite object ωp2 indicative by deductive reasoning of a second plausibility value for the target rule L.