Complementizer

In linguistics (especially generative grammar), complementizer or complementiser (glossing abbreviation: ) is a functional category (part of speech) that includes those words that can be used to turn a clause into the subject or object of a sentence. For example, the word "that" may be called a complementizer in English sentences like "Mary believes that it is raining". The concept of complementizers is specific to certain modern grammatical theories; in traditional grammar, such words are normally considered conjunctions. The standard abbreviation for "complementizer" is C. 
Category of C.
C as head of CP.
The complementizer is often held to be the syntactic head of a full clause, which is therefore often represented by the abbreviation CP (for "complementizer phrase"). Evidence that the complementizer functions as the head of its clause includes that it is commonly the last element in a clause in head-final languages like Korean or Japanese, in which other heads follow their complements, whereas it appears at the start of a clause in head-initial languages such as English, where heads normally precede their complements. The trees below illustrate the phrase "Taro said that he married Hanako" in Japanese and English; syntactic heads are marked in red, demonstrating that C falls in head-final position in Japanese, and in head-initial position in English. 
Sources of C.
It is common for the complementizers of a language to develop historically from other syntactic categories, a process known as grammaticalization.
C can develop from a determiner.
Across the languages of the world, it is especially common for pronouns or determiners to be used as complementizers (e.g., English "that").
"I read in the paper that it's going to be cold today."
C can develop from an interrogative word.
Another frequent source of complementizers is the class of interrogative words. It is especially common for a form that otherwise means "what" to be borrowed as a complementizer, but other interrogative words are often used as well, as in the following colloquial English example, where unstressed "how" is roughly equivalent to "that".
"I read in the paper how it's going to be cold today."
C can develop from a preposition.
With non-finite clauses, English "for" in sentences like "I would prefer for there to be a table in the corner" shows a preposition that has arguably developed into a complementizer. (The sequence "for there" in this sentence is not a prepositional phrase under this analysis.)
C can develop from a verb.
In many languages of West Africa and South Asia, the form of the complementizer can be related to the verb "say". In these languages, the complementizer is also called the quotative. The quotative performs many extended functions in these languages.
Empty complementizers.
Some analyses allow for the possibility of invisible or "empty" complementizers. An empty complementizer is considered to be present when there is not a word, even though the rules of grammar expect one. The complementizer (for example, "that") is usually said to be understood – "i.e.", an English speaker knows it is there, and so it does not need to be said. Its existence in English has been proposed based on the following type of alternation:
Because "that" can be inserted between the verb and the embedded clause without changing the meaning, the original sentence without a visible complementizer would be reanalyzed as
Where the symbol "∅C" represents the empty (or "null") complementizer, this suggests another interpretation of the earlier "how" sentence:
where "how" serves as a specifier to the empty complementizer. This allows for a consistent analysis of another troublesome alternation:
where "OP" represents an invisible interrogative known as an operator.
In a more general sense, the proposed empty complementizer parallels the suggestion of near-universal empty determiners.
Various analyses have been proposed to explain when the empty complementizer ∅ can substitute for a phonologically overt complementizer. One explanation is that complementizers are eligible for omission when they are epistemically neutral or redundant. For example, in many environments, English's epistemically neutral that and Danish's at can be omitted. In addition, if a complementizer expresses a semantic meaning that is also expressed by another marker in the phrase, the complementizer carrying the redundant meaning may be omitted. Consider the complementizer be in Mangap-Mbula, which expresses uncertainty, in the following example: 
Here, the marker ko also expresses epistemic uncertainty, so be can be replaced by the phonologically null complementizer without affecting meaning or grammaticality.
Complementizers are present in a wide range of environments; in some, C is obligatorily overt (i.e., cannot be replaced by the empty complementizer). For example, in English, CPs selected for by manner-of-speaking verbs ("whisper, mutter, groan", etc) resist C-drop:
In other environments, the complementizer can be omitted without loss of grammaticality, but may result in semantic ambiguity. For example, consider the English sentence "The newspaper reported that a new mayor was elected and" ("that) "there was a riot." Listeners can infer a causal relationship between the two events reported by the newspaper: a new mayor was elected, and as a result, there was a riot. Alternatively, the events may be interpreted as independent of each other. The non-causal interpretation is more likely when the second complementizer that" is present, whereas the causal interpretation is more likely when an empty complementizer is present. 
The ambiguity here arises because the sentence where the second complementizer is empty may also be interpreted as simply having no second complementizer. In the first case, the sentence involves coordination of CPs, which lends itself more easily to a non-causal interpretation, but the latter case involves coordination of TPs, which is the necessary structure for a causal interpretation. Partial syntax trees for the possible structures are given below. 
Selectional restrictions imposed by C.
As a syntactic head, C always selects for a complement tense phrase (TP) whose syntax and semantics are dictated by the choice of C. The choice of C can determine whether the associated TP is finite or non-finite, whether it carries the semantic meaning of certainty or uncertainty, whether it expresses a question or an assertion, et cetera.
Propositions vs. indirect questions.
The following complementizers are available in English: that, for, if, whether, ∅. 
If and whether form CPs that express indirect questions:
In contrast, complementizers for, that," as well as the phonologically null complementizer ∅" introduce "declarative or non-interrogative" CPs.
Finite vs. non-finite TPs.
Tense phrases in English can be divided into finite (tensed) clauses or non-finite (tenseless) clauses. The former includes an indication of the relative time when its content occurs; the latter has no overt indication of time: compare "John will leave" (John's leaving will take place in the future) with "John wants to leave" (we are unsure when John is leaving). 
Certain complementizers strictly select for finite clauses (denoted [+finite]) while others select for non-finite clauses (denoted [-finite]).
Complementizers if, that require [+tense] TP:
Complementizer for requires a [-tense] TP:
Complementizer whether allows either [+tense] or [-tense] TP:
Epistemic selection.
Complementizers frequently carry epistemic meaning - that is, meaning about the speaker's degree of certainty (for example, whether they are doubtful), or the speaker's source of information (for example, whether they are making an inference, or have direct evidence). Contrast the meaning of "if" and "that" in English:
“If” signals that the associated tense phrase must carry the epistemic meaning of uncertainty. In contrast, “that” is epistemically neutral. This contrast is not uncommon cross-linguistically: in languages with only two complementizers, one is frequently neutral, while the other carries the meaning of uncertainty. One such language is Lango (a Nilotic language spoken in Uganda):
Additional languages with this neutrality/uncertainty complementizer contrast include several European languages:
In other languages, complementizers are richer in epistemic meaning. For example, in Mangap-Mbula, an Austronesian language of Papua New Guinea, the following complementizers are available:
More generally, complementizers have been found to express the following values cross-linguistically: certainty, (general) uncertainty, probability, negative probability/falsehood, apprehension, and reportativity.
Complementizers in Itzaj Maya also demonstrate epistemic meaning. For instance, English "that" and Itzaj Maya "kej" are used not only to identify complements, but also to introduce relative clauses:
Itzaj Maya (Hofling, 2000: 496, 495)
(1) a.
Taken from Boye (2015), page 3 
(1) b. 
Taken from Boye (2015), page 3 
(1a) introduces a subordinate clause and (1b) introduces a conditional clause, similar to English. The former subtype "that" can be defined in terms of "information source" and includes meanings glossed as direct evidence, indirect evidence, hearsay, inferential. The latter one "if" can be defined in terms of "degree of certainty" and includes meanings glossed as certainty, probability, epistemic possibility, doubt. Thus, epistemic meaning as a whole can be defined in terms of the notion of "justificatory support".
Abbreviations adapted from Boye (2015) page 15 and Hofling (1998) page 225-226.
Complementizer stacking.
But not only that, Itzaj Maya can combine the neutral complementizer "ke" with the non-neutral, "waj." This is illustrated in examples (2a), where the neutral complementizer "ke" occurs alone, and (2b), where it is optionally inserted in front of the uncertainty complementizer "waj:"
Itzaj Maya (Hofling, 2000: 495, 506)
(2) a.
Taken from Boye (2015), page 9
(2) b.
Taken from Boye (2015), page 9 
In (1a,b) and (2a) we saw each complementizer can be licensed once within the clause, but in (2b) we observe the significant difference of Itzaj Maya from English. In English we are able to license multiple C as long as the clause is completed with the embedded V or D. For example, I saw that fox that ran towards the garden that Tommy took care of. In such cases, C can appear as the complement of V or D many times. However, CP-recursion in two tiers or CP appearing as an immediate complement of maximal projection CP cannot be allowed in English. This action of "Complementizer Stacking" is realised as ungrammatical. 
In Scandinavian languages, however, we see this phenomenon of complementizer stacking. For example, researchers observed the two basic types of CP-recursion that occur independently in Danish: a CP with V2 (i.e. a CP headed by a lexical predicate in its head position) will be referred as CP ("big CP"), whereas a CP without V2 (i.e. CP headed by a non-lexical element) will be referred to as cP ("little cP"). 
Adapted from Nyvad et al., (2017) page 453.
The case of little/big CPs are comparable to "VP shell" structure in English where it introduces a small v in the higher position in the tree, and big V in the lower position in the tree.
We also see in the examples, Danish allows complementizer stacking in constructions involving subject extraction from complement and relative clauses in colloquial speech:
(3) a.
(3) b.
Taken from Nyvad et al., (2017) page 463-464
We observe that complementizers are indeed stacked together in the beginning of the clause, acting as a complement of DP. CP-recusion structure on the right is applied for each of the clause, which points to evidence of complementizer stacking in Danish. In addition, we note the combination of "som at der" in (3a) is only possible in one specific order, which lead the researchers to believe that s"om" may not require an empty operator in its Spec-CP position.
In various languages.
Assyrian Neo-Aramaic.
In Assyrian Neo-Aramaic, a modern Aramaic language, (or , depending on the dialect) is used as a complementizer and is related to the relativizer. Though it is less common in casual speech, and more so in formal conversation.
Hebrew.
In Hebrew (both Modern and Ancient) two complementizers coexist: שֶ , which is either related to the relativizer "‘asher" ( &lt; Akkadian "‘ashru" ‘place’) and/or to the pronominal Proto-Semitic "dhu" ('this'); and כִּי [ki], which is also used as a conjunction meaning 'because, when'. In modern usage, the latter is reserved for more formal writing.
American Sign Language.
While some manual complementizers exist in American Sign Language they are usually expressed non-manually by facial expressions. Conditional clauses, for example, are indicated by raised eye-brows. If a manual complementizer is used it is also accompanied by a facial expression. The non-manual marking of complementizers is a common phenomenon found in many sign languages and it has even been suggested by Fabian Bross that C-categories are universally marked with the face in sign languages.