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27
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 20 (9 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.
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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Cited by 7 (3 self)
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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
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 7 (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.
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
The NPCompleteness 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 w ..."
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Cited by 4 (3 self)
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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 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. 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 justification
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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Cited by 3 (3 self)
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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
Intelligent Players
 CUNY Ph.D. Program in Computer Science
, 1976
"... Rational decisions depend on what players know, hence an appropriate epistemic analysis is an integral element of the foundations of Game Theory. We suggest a general logical approach for studying games which consists of formalizing rationality and games in epistemic logic and deriving their propert ..."
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Cited by 3 (1 self)
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Rational decisions depend on what players know, hence an appropriate epistemic analysis is an integral element of the foundations of Game Theory. We suggest a general logical approach for studying games which consists of formalizing rationality and games in epistemic logic and deriving their properties in the resulting logical system. We study a number of examples and demonstrate that our model can produce a finergrained analysis of gametheoretical scenarios and provide a noncircular justification of Nash equilibrium strategies. We show that within this model, in strategicform and extensiveform games, an assumption of firstlevel mutual knowledge of the game and players ’ rationality implies Nash equilibrium and backward induction solutions. This refutes a general perception that common knowledge of rationality is needed to justify backward induction in games with perfect information. 1
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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Cited by 3 (0 self)
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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
Why do we need Justification Logic
 Norms and Reasons: Logic at the Crossroads, Synthese Library 353
, 2011
"... In this paper, we will sketch the basic system of Justification Logic, which is a general logical framework for reasoning about epistemic justification. Justification Logic renders a new, evidencebased foundation for epistemic logic. As a case study, we compare formalizations of the Kripke ‘Red Bar ..."
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Cited by 3 (0 self)
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In this paper, we will sketch the basic system of Justification Logic, which is a general logical framework for reasoning about epistemic justification. Justification Logic renders a new, evidencebased foundation for epistemic logic. As a case study, we compare formalizations of the Kripke ‘Red Barn ’ scenario in modal epistemic logic and Justification Logic and show here that the latter provides a deeper analysis. In particular, we argue that modal language fails to fully represent the epistemic closure principle whereas Justification Logic provides its adequate formalization. 1