Linear temporal justification logics with past and future time modalities

Logic Journal of the IGPL 31 (1):1-38 (2023)
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Abstract

Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov’s logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, one based on interpreted systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem.

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Meghdad Ghari
University Of Isfahan

References found in this work

Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Logics of Time and Computation.Robert Goldblatt - 1990 - Studia Logica 49 (2):284-286.
Justification logic.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
Justifications for common knowledge.Samuel Bucheli, Roman Kuznets & Thomas Studer - 2011 - Journal of Applied Non-Classical Logics 21 (1):35-60.

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