Self-referentiality of Justified Knowledge

  • Roman Kuznets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


The principal result of Justification Logic is the Realization Theorem, which states that behind major epistemic modal logics there are corresponding systems of evidence/justification terms sufficient for reading all provable knowledge assertions as statements about justifications. A knowledge/belief modality is self-referential if there are modal sentences that cannot be realized without using self-referential evidence of type “t is a proof of A(t).” Building on an earlier result that S4 and its justification counterpart Open image in new window describe knowledge that is self-referential, we show that the same is true for Open image in new window , Open image in new window , and Open image in new window with their justification counterparts whereas for Open image in new window and Open image in new window self-referentiality can be avoided. Therefore, no single modal axiom from the standard axiomatizations of these logics is responsible for self-referentiality.


Modal Logic Auxiliary Variable Closure Condition Modal Rule Axiom Scheme 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roman Kuznets
    • 1
  1. 1.Ph.D. Program in Computer ScienceCUNY Graduate CenterNew YorkUSA

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