Decidability for Justification Logics Revisited

Abstract

Abstract. Justification logics are propositional modal-like logics that instead of statements A is known include statements of the form A is known for reason t where the term t can represent an informal justification for A or a formal proof of A. In our present work, we introduce model-theoretic tools, namely: filtrations and a certain form of generated submodels, in the context of justification logic in order to obtain decidability results. Apart from reproving already known results in a uniform way, we also prove new results. In particular, we use our submodel construction to establish decidability for a justification logic with common knowledge for which so far no decidability proof was available.

Weak arithmetical interpretations for the Logic of Proofs

“…The notion of an almost schematic constant specification goes back to Kuznets [Kuz08]. For recent presentations of various decidability results, see [BKS13,Stu12,Stu13].…”

Justification logic enjoys the strong finite model property

“…Given the proof of Lemma 8 in [8] it is easy to see that we can effectively compute bounds on the size of the finitary model. Thus we get the strong finitary model property as a corollary of Lemma 8.…”

“…There are many known decidability results for justification logics, see, for instance, [8,11,15]. However, many of these decidability proofs rely on completeness with respect to a recursively enumerable class of models and Post's theorem [14].…”