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FirstOrder Logic of Proofs
, 2011
"... The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP capa ..."
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Cited by 28 (12 self)
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The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP capable of realizing firstorder modal logic S4 and, therefore, the firstorder intuitionistic logic HPC. FOLP enjoys a natural provability interpretation; this provides a semantics of explicit proofs for firstorder S4 and HPC compliant with BrouwerHeytingKolmogorov requirements. FOLP opens the door to a general theory of firstorder justification.
Justified Belief Change
, 2010
"... Justification Logic is a framework for reasoning about evidence and justification. Public Announcement Logic is a framework for reasoning about belief changes caused by public announcements. This paper develops JPAL, a dynamic justification logic of public announcements that corresponds to the modal ..."
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Cited by 8 (8 self)
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Justification Logic is a framework for reasoning about evidence and justification. Public Announcement Logic is a framework for reasoning about belief changes caused by public announcements. This paper develops JPAL, a dynamic justification logic of public announcements that corresponds to the modal theory of public announcements due to Gerbrandy and Groeneveld. JPAL allows us to reason about evidence brought about by and changed by Gerbrandy–Groeneveldstyle public announcements.
Justifications for common knowledge
 Journal of Applied Nonclassical Logics
, 2011
"... ABSTRACT. Justification logics are epistemic logics that explicitly include justifications for the agents ’ knowledge. We develop a multiagent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripkestyle semantics that is similar to Fitting ..."
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Cited by 8 (6 self)
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ABSTRACT. Justification logics are epistemic logics that explicitly include justifications for the agents ’ knowledge. We develop a multiagent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripkestyle semantics that is similar to Fitting’s semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multiagent justification logic with respect to this Kripkestyle semantics. We demonstrate that our logic is a conservative extension of Yavorskaya’s minimal bimodal explicit evidence logic, which is a twoagent version of LP. We discuss the relationship of our logic to the multiagent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.
Knowledgebased rational decisions
 CUNY Ph.D. Program in Computer Science
, 2009
"... We outline a mathematical model of rational decisionmaking based on standard gametheoretical assumptions: 1) rationality yields a payoff maximization given the player’s knowledge; 2) the standard logic of knowledge for Game Theory is the modal logic S5. Within this model, each game has a solution ..."
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We outline a mathematical model of rational decisionmaking based on standard gametheoretical assumptions: 1) rationality yields a payoff maximization given the player’s knowledge; 2) the standard logic of knowledge for Game Theory is the modal logic S5. Within this model, each game has a solution and rational players know which moves to make at each node. We demonstrate that uncertainty in games of perfect information results exclusively from players ’ different perceptions of the game. In strictly competitive perfect information games, any level of players ’ knowledge leads to the backward induction solution which coincides with the maximin solution. The same result holds for the wellknown centipede game: its standard ‘backward induction solution ’ does not require any mutual knowledge of rationality. 1
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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Cited by 5 (4 self)
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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
The ontology of justifications in the logical setting
 Studia Logica
, 2012
"... Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets ..."
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Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models. We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient premodels of the former. 1
The NPCompleteness of Reflected Fragments of Justification Logics
, 2009
"... 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 just ..."
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Cited by 4 (3 self)
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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 socalled 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 NPcomplete, thereby proving a matching lower bound.
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.
Reasoning About Games
 Studia Logica
"... A mixture of propositional dynamic logic and epistemic logic is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [4, 5, 6, 7]. We call the (family of) logics used here PDL + E. It is in the general family of Dynamic Epistemic Logics [21], was applie ..."
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A mixture of propositional dynamic logic and epistemic logic is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [4, 5, 6, 7]. We call the (family of) logics used here PDL + E. It is in the general family of Dynamic Epistemic Logics [21], was applied to games already in [20], and investigated further in [18, 19]. Epistemic states of players, usually treated informally in gametheoretic arguments, are here represented explicitly and reasoned about formally. The heart of the presentation is a detailed analysis of the Centipede game using both the proof theoretic and the semantic machinery of PDL + E. The present work can be seen partly as an argument for the thesis that PDL + E should be the basis of the logical investigation of game theory. 1