Partial realization in dynamic justification logic

Abstract. Justification logic is an epistemic framework that provides a way to express explicit justifications for the agent’s belief. In this paper, we present OPAL, a dynamic justification logic that includes term operators to reflect public announcements on the level of justifications. We create dynamic epistemic semantics for OPAL. We also elaborate on the relationship of dynamic justification logics to Gerbrandy–Groeneveld’s PAL by providing a partial realization theorem.

The NP-Completeness of Reflected Fragments of Justification Logics

Abstract. Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. 1 Introduction and Main Definitions Justification Logic is an emerging field that studies provability, knowledge, and belief via explicit proofs or justifications that are part of the language. A justificatio

Decidability for Justification Logics Revisited

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

Justified terminological reasoning

Justification logics are epistemic logics that include explicit justifications for an agent’s knowledge. In the present paper, we introduce a justification logic J ALC over the description logic ALC. We provide a deductive system and a semantics for our logic and we establish soundness and completeness results. Moreover, we show that our logic satisfies the so-called internalization property stating that it internalizes its own notion of proof. We then sketch two applications of J ALC: (i) the justification terms can be used to generate natural language explanations why an ALC statement holds and (ii) the terms can be used to study data privacy issues for description logic knowledge bases

alpha-logic

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Formal considerations on Gabbay's restart rule in natural deduction and goal-directed reasoning

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