Self-referentiality of Justified Knowledge
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.
KeywordsModal Logic Auxiliary Variable Closure Condition Modal Rule Axiom Scheme
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