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The eighth International сonference "Advances in Modal Logic" (AiML 2010)
August 25, 2010 12:25, Moscow
 


A syntactic realization theorem for justification logics

Kai Brünnler, Remo Goetschi, Roman Kuznets
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Kai Brünnler, Remo Goetschi, Roman Kuznets


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Abstract: Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms $d$, $t$, $b$, $4$, and $5$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for $KB5$ and $S5$ by showing that the positive introspection operator is superfluous.

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