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Paper   IPM / M / 17614
School of Mathematics
  Title:   Tableaux and interpolation for propositional justification logics
  Author(s):  Meghdad Ghari
  Status:   Published
  Journal: Notre Dame J. Formal Logic
  Vol.:  65
  Year:  2024
  Pages:   81-112
  Supported by:  IPM
  Abstract:
In this paper, we present tableau proof systems for the annotated version of propositional justification logics; that is, justification logics which are formulated using annotated application operators. We show that the tableau systems are sound and complete with respect to Mkrtychev models, and some tableau systems are analytic and provide a decision procedure for the annotated justification logics. We further show Craigâ??s interpolation property and Bethâ??s definability theorem for some annotated justification logics.

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