Justification logics, logics of knowledge, and conservativity


Authors
Melvin Fitting
CUNY Graduate Center
Abstract
Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open.
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Justifications for Common Knowledge.Samuel Bucheli, Roman Kuznets & Thomas Studer - 2011 - Journal of Applied Non-Classical Logics 21 (1):35-60.
Logic of Implicit and Explicit Justifiers.Alessandro Giordani - 2016 - In L. Felline, A. Ledda, F. Paoli & E. Rossanese (eds.), New Directions in Logic and the Philosophy of Science. College Publications. pp. 119-131.
A New Framework for Justification Logic.Alessandro Giordani - 2015 - Journal of Applied Non-Classical Logics 25 (4):308-323.
Labeled Sequent Calculus for Justification Logics.Meghdad Ghari - 2017 - Annals of Pure and Applied Logic 168 (1):72-111.

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