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|Paper IPM / M / 16730||
Temporal justification logic is a new family of temporal logics of knowledge
in which the knowledge of agents is modeled 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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