Annals of Pure and Applied Logic 152 (1):67-83 (2008)
A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works 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 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
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References found in this work BETA
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
The Logic of Proofs, Semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
Provability Logics with Quantifiers on Proofs.Rostislav E. Yavorsky - 2001 - Annals of Pure and Applied Logic 113 (1-3):373-387.
Citations of this work BETA
The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence.Alexandru Baltag, Bryan Renne & Sonja Smets - 2014 - Annals of Pure and Applied Logic 165 (1):49-81.
The Ontology of Justifications in the Logical Setting.Sergei N. Artemov - 2012 - Studia Logica 100 (1-2):17-30.
From the Knowability Paradox to the Existence of Proofs.W. Dean & H. Kurokawa - 2010 - Synthese 176 (2):177 - 225.
Discovering Knowability: A Semantic Analysis.Sergei Artemov & Tudor Protopopescu - 2013 - Synthese 190 (16):3349-3376.
The Paradox of the Knower Revisited.Walter Dean & Hidenori Kurokawa - 2014 - Annals of Pure and Applied Logic 165 (1):199-224.
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