Update Rules and Semantic Universals

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Abstract
We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible functions of the relevant type, only few appear in the lexicon of natural languages: the connectives in English, for example, are only 'and', 'or', and perhaps 'nor' (expressing negated disjunction). The logically possible 'nand' (negated conjunction) is not expressed by a lexical entry of English, or of any natural language. The explanation we propose is based on the “dynamic” behaviour of connectives and quantifiers: we define update potentials for logical operator, under the assumption that the logical structure of a sentence p defines what type of update p contributes to context, together with the speech act performed (assertion or denial). We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language.
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Archival date: 2020-08-15
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2020-08-15

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