The paper provides a technique for algorithmic syntax-semantics interface in computational grammar with underspecified semantic representations of human language. The technique is introduced for expressions that contain NP quantifiers, by using computational, generalised Constraint-Based Lexicalised Grammar (GCBLG) that represents major, common syntactic characteristics of a variety of approaches to formal grammar and natural language processing (NLP). Our solution can be realised by any of the grammar formalisms in the CBLG class, e.g., Head-Driven Phrase Structure Grammar (HPSG), Lexical Functional Grammar (LFG), Categorial Grammar (CG). The type-theory of acyclic recursion L_(ar)~λ, provides facility for representing major semantic ambiguities, as under-specification, at the object level of the formal language of L_(ar)~λ, without recourse of meta-language variables. Specific semantic representations can be obtained by instantiations of underspecified L_(ar)~λ terms, in context. These are subject to constraints provided by a newly introduced feature-structure description of syntax-semantics interface in GCBLG.
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