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Title: A Completeness Result for the Implicit Justification STIT Logic
Author(s): OLKHOVIKOV, Grigory K.
Journal: Logique et Analyse
Volume: 243 Date: 2018
We present a completeness result for the implicit fragment of justification stit logic introduced in . 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.