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| Paper IPM / M / 16730 |
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| Abstract: | |
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Temporal justi fication logic is a new family of temporal logics of knowledge
in which the knowledge of agents is modeled using a justi fication logic. In this paper we
present various temporal justifi cation 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 justifi cation and time.
We present two kinds of semantics for our temporal justi fication 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 justi fication logics. We further investigate the two
well-known epistemic-temporal notions of no forgetting and no learning in the framework
of justi fication logics. Finally, we present temporal justi fication logics that avoid the
logical omniscience problem.
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