A completeness result for the implicit justification stit logic

Grigori K. Olkhovikov


We present a completeness result for the implicit fragment of justification stit logic introduced in [16]. Implicit justification stit logic merges the structures of stit logic with the structures of epistemic justification logic and adds to this mix two new modalities, ‘agent j proves A’ and ‘A is proven’. Although this logic allows for no strongly complete axiomatization, we show that a restricted form of strong completeness (subsuming weak completeness) is available, as well as deduce a version of the restricted compactness property. We also briefly address the question of whether implicit justification stit logic is a conservative extension of stit and epistemic justification logic, and under what conditions the lifting lemma of justification logic will be provable also in implicit jstit logic.

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