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Based on the principle of compositionality, it is easy to write a grammar which builds the syntax and the semantics of a phrase in parallel: it suffices to pair with each syntactic a semantic rule specifying how to build up the meaning of the constituent from the meaning of its parts. Computationally, Unification-Based grammars provide an easy way to integrate syntax and semantics. The feature structures representing the categories of linguistic constituent simply contain both a syntax and a semantics attribute the value of which reflect the syntactic and semantic information associated by the grammar with that constituent.
Traditionally, the semantic representation of a phrase is a lambda-term whose model theoretic interpretation models the meaning of that phrase. This is the view that was developed by Montague. However more recently, there has been a worry that such a framework is computationally intractable (and cognitively implausible) in that it enumerates all the possible readings of a constituent. Since ambiguity is a pervasive feature of natural language, this directly leads to a combinatorial explosion: a sentence with n scope bearing elements will have n! readings. The idea to delay the enumeration of reading has lead to the area of semantic underspecification.
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