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Partial realization in dynamic justification logic
 Logic, Language, Information and Computation, 18th International Workshop, WoLLIC 2011
"... 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 ..."
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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. 1
Decidability for some Justification Logics with Negative Introspection
, 2011
"... Justification logics are modal logics that include justifications for the agent’s knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logi ..."
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Justification logics are modal logics that include justifications for the agent’s knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications. 1
Justifications, Ontology, and Conservativity
"... Artemov recently presented an ontologically transparent semantics for justifications that interprets justifications as sets of formulas they justify. However, this semantics of modular models has only been studied for the case of the basic justification logic J, corresponding to the modal logic K, a ..."
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Artemov recently presented an ontologically transparent semantics for justifications that interprets justifications as sets of formulas they justify. However, this semantics of modular models has only been studied for the case of the basic justification logic J, corresponding to the modal logic K, and it has been left open how to extend modular models to and relate them to the already existing symbolic and epistemic semantics for justification logics with additional axioms, in particular, for logics of knowledge with factive justifications. We introduce modular models for extensions of J with any combination of the axioms (jd), (jt), (j4), (j5), and (jb), which are the explicit counterparts of standard modal axioms. After establishing soundness and completeness results, we examine the relationship of modular models to the more traditional symbolic and epistemic models. This comparison yields several new semantics, including symbolic models for logics of belief with negative introspection (j5) and models for logics with axiom (jb). Besides pure justification logics we also consider logics with both justifications and a belief/knowledge modal operator of the same strength. In particular, we use modular models to study the conditions under which the addition of such an operator to a justification logic yields a conservative extension.
Decidability for Justification Logics Revisited
"... Justification logics are propositional modallike 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 modeltheoretic tools, name ..."
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Justification logics are propositional modallike 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 modeltheoretic 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
 PSI 11. PROCEEDINGS OF THE 8TH ANDREI ERSHOV INFORMATICS CONFERENCE, LNCS
"... 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 complet ..."
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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 socalled 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.
Realizing Public Announcements by Justifications
, 2012
"... Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent’s belief. We present OPAL(K) and JPAL( ..."
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Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent’s belief. We present OPAL(K) and JPAL(K), two alternative justification counterparts of Gerbrandy–Groeneveld’s public announcement logic PAL(K). We show that PAL(K) is the forgetful projection of OPAL(K), respectively of JPAL(K), and we establish that JPAL(K) partially realizes PAL(K). The question whether a similar result also holds for OPAL(K) is still open. 1
Justification Logic, Inference Tracking, and Data Privacy
"... Internalization is a key property of justification logics. It states that justification logics internalize their own notion of proof which is essential for the proof of the realization theorem. The aim of this note is to show how to make use of internalization to track where an agent’s knowledge com ..."
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Internalization is a key property of justification logics. It states that justification logics internalize their own notion of proof which is essential for the proof of the realization theorem. The aim of this note is to show how to make use of internalization to track where an agent’s knowledge comes from and how to apply this to the problem of data privacy.
Update As Evidence: Belief Expansion
"... We introduce a justification logic with a novel constructor for evidence terms, according to which the new information itself serves as evidence for believing it. We provide a sound and complete axiomatization for belief expansion and minimal change and explain how the minimality can be graded acc ..."
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We introduce a justification logic with a novel constructor for evidence terms, according to which the new information itself serves as evidence for believing it. We provide a sound and complete axiomatization for belief expansion and minimal change and explain how the minimality can be graded according to the strength of reasoning. We also provide an evidential analog of the Ramsey axiom.