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- W1972836303 abstract "A propositional logic of explicit proofs, LP , was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 (1) (2001) 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman (Ed.), Kurt Gödel Collected Works (Oxford, 1986–2003, five volumes) III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. A major result about LP is the Realization Theorem, that says any theorem of S4 can be converted into a theorem of LP by some replacement of necessitation symbols with explicit proof terms. Thus the necessitation operator of S4 can be seen as a kind of implicit existential quantifier: there exists a proof term (explicit evidence) such that…. In this paper, quantification over evidence is introduced into LP , and it is shown that the connection between S4 necessitation and the existential quantifier becomes an explicit one. The extension of LP with quantifiers is called QLP . A semantics and an axiom system for QLP are given, soundness and completeness are established, and several results are proved relating QLP to LP and to S4 ." @default.
- W1972836303 created "2016-06-24" @default.
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- W1972836303 date "2008-03-01" @default.
- W1972836303 modified "2023-09-30" @default.
- W1972836303 title "A quantified logic of evidence" @default.
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- W1972836303 doi "https://doi.org/10.1016/j.apal.2007.11.003" @default.
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