Abstract
We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical object. More common is the situation, corresponding tounderspecification, in which there is more than one model. A situation inwhich there are no models corresponds to an ungrammatical input.
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Muskens, R. Talking about Trees and Truth-Conditions. Journal of Logic, Language and Information 10, 417–455 (2001). https://doi.org/10.1023/A:1017912606063
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DOI: https://doi.org/10.1023/A:1017912606063