by a homomorphism between an algebra of syntactic representations and an algebra of semantic objects. The principle of compositionality also exists in a similar form in the compositionality of programming languages. Critiques The principle of compositionality has been the subject of intense debate. Indeed, there is no general agreement as to how the principle is to be interpreted, although there have been several attempts to provide formal definitions of it. Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical testing; an analytic truth, obvious from the nature of language and meaning; or a methodological principle to guide the development of theories of syntax and semantics. The Principle of Compositionality has been attacked in all three spheres, although so far none of the criticisms brought against it have been generally regarded as compelling. Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language. The principle of compositionality usually holds when only syntactic factors play in the increased complexity of sentence processing, while it becomes more problematic and questionable when the complexity increase is due to sentence or discourse context, semantic memory, or sensory cues. Among the problematic phenomena for traditional theories of compositionality is that of logical metonymy, which has been studied at least since the mid 1990s by linguists James Pustejovsky and Ray Jackendoff. Logical metonymies are sentences like John began the book, where the verb to begin requires (subcategorizes) an event as its argument, but in a logical metonymy an object (i.e. the book) is found instead, and this forces to interpret the sentence by inferring an implicit event ("reading", "writing", or other prototypical actions performed on a book). The problem for compositionality is that the meaning of reading or writing is not present in the words of the sentence, neither in "begin" nor in "book". Further, in the context of the philosophy of language, the principle of compositionality does not explain all of meaning. For example, you cannot infer sarcasm purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. Thus, some theorists argue that the principle has to be revised to take into account linguistic and extralinguistic context, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.