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A partial logic of descriptions Apostoli, Peter J.


Let a "partial logic" for a first order predicate language L be a formal proof-theory PT for sentences of L together with a model theoretic semantics for PT which can be considered a generalization of classical first-order Tarskian semantics in the following sense: if M is a model for PT then M is a partial function from the set of sentences of L into the set {T, F} of classical truth values such that 1) every atomic sentence of L receives exactly one truth value, and 2) if M agrees with a given Tarskian model TM on the assignment of truth values to the atomic sentences of L, then M agrees with TM everywhere M is defined. In this paper we utilize formal techniques developed by P. C. Gilmore for intensional set theories without excluded middle to present a sound and complete partial logic Pld for the first order predicate calculus with definite descriptions. Pld utilizes truth value gaps to systematically treat symbolic sentences that contain "improper" description terms, and can be seen as an acceptable formalization of the Strawsonian view that the semantic-well-formedness of a grammatically subject-predicate sentence of English presupposes the propriety of any definite description occurring as subject term therein.

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