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Paper   IPM / M / 16730
School of Mathematics
  Title:   Linear temporal justifiCation logics with past and future time modalities
  Author(s):  Meghdad Ghari
  Status:   Published
  Journal: Log. J. IGPL
  Vol.:  31
  Year:  2023
  Pages:   1-38
  Supported by:  IPM
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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