Reasoning with justifications

This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a natural way long-standing problems of logical omniscience. Since then, LP has become one member of a family of related logics, all logics of knowledge with explicit knowledge terms. In this paper the original problem of intuitionistic foundations is discussed only briefly. We concentrate entirely on issues of reasoning about knowledge.
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Realizations and LP.Melvin Fitting - 2009 - Annals of Pure and Applied Logic 161 (3):368-387.
Non-Circular Proofs and Proof Realization in Modal Logic.Ren-June Wang - 2014 - Annals of Pure and Applied Logic 165 (7-8):1318-1338.

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