Logic Journal of the IGPL 24 (5):743-773 (2016)

Meghdad Ghari
University Of Isfahan
Justification logics provide a framework for reasoning about justifications and evidence. In this article, we study a fuzzy variant of justification logics in which an agent’s justification for a belief has certainty degree between 0 and 1. We replace the classical base of justification logics with Hájek’s rational Pavelka logic. We introduce fuzzy possible world semantics with crisp accessibility relation and also single world models for our logics. We establish soundness and graded-style completeness for both kinds of semantics. We also introduce extensions with product conjunction. Finally, we offer a solution to a variant of the sorites paradox in our fuzzy justification logics.
Keywords Justification logic  Łukasiewicz logic  rational Pavelka logic  soundness  graded-style completeness  sorites paradox
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Reprint years 2016
DOI 10.1093/jigpal/jzw019
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References found in this work BETA

The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
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.

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Citations of this work BETA

Temporal Justification Logic.S. Bucheli, M. Ghari & T. Studer - 2017 - Proceedings of the Ninth Workshop on Methods for Modalities (M4M9 2017), Indian Institute of Technology, Kanpur, India, 8th to 10th January 2017, Electronic Proceedings in Theoretical Computer Science 243, Pages 59–74.

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