Underspecified semantics

In Klaus von Heusinger & Urs Egli (eds.), Reference and Anaphoric Relations. Kluwer Academic Publishers. pp. 311--338 (2000)
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Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings first and testing their acceptability afterwards will not be feasible. This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models.
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Model Theory.Makkai, Michael; Chang, C. C. & Keisler, H. J.
Generalized Phrase Structure Grammar.Gazdar, Gerald; Klein, Ewan; Pullum, Geoffrey & Sag, Ivan

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