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 … Show more
“…The notion of an almost schematic constant specification goes back to Kuznets [Kuz08]. For recent presentations of various decidability results, see [BKS13,Stu12,Stu13].…”
Abstract. Artemov established an arithmetical interpretation for the Logics of Proofs LP CS , which yields a classical provability semantics for the modal logic S4.
“…The notion of an almost schematic constant specification goes back to Kuznets [Kuz08]. For recent presentations of various decidability results, see [BKS13,Stu12,Stu13].…”
Abstract. Artemov established an arithmetical interpretation for the Logics of Proofs LP CS , which yields a classical provability semantics for the modal logic S4.
“…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.…”
Section: ν| ≤ H(|a|)mentioning
confidence: 99%
“…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].…”
We observe that justification logic enjoys a form the strong finite model property (sometimes also called small model property). Thus we obtain decidability proofs for justification logic that do not rely on Post's theorem.
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