Same Same But Different: An Alphabetically Innocent Compositional Predicate Logic
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Compositionality is at the heart of model theoretical semantics and its application to the semantics of natural language. As has become standard practice, linguists translate a fragment of English into an intensional extension of classical predicate logic (PL). Yet, somewhat ironically and strangely, PL itself is not compositional, because the standard truth conditions for quantificational statements are not a function of the denotations of its parts but depend on value assignments for variables. This kind of dependence on value assignments leads to non-compositionality as will be demonstrated explicitly in Section 1.2. One could, as is well-known, remedy this awkwardness by considering not truth values as denotations of formulas but sets of value assignments for variables. As we will show in Section 1.3, such a semantics is compositional but not “alphabetically invariant” (or “innocent”). In this article we will formulate a compositional extension of PL that...
KeywordsFree Variable Semantic Feature Predicate Logic Semantic Role Assignment Function
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