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The logic of proofs, semantically
 Annals of Pure and Applied Logic
, 2005
"... web page: comet.lehman.cuny.edu/fitting ..."
Evidencebased common knowledge
 CUNY Ph.D. Program in Computer Science Technical Reports
, 2004
"... In this paper we introduce a new type of knowledge operator, called evidencebased knowledge, intended to capture the constructive core of common knowledge. An evidencebased knowledge system is obtained by augmenting a multiagent logic of knowledge with a system of evidence assertions t:ϕ (“t is an ..."
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Cited by 43 (11 self)
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In this paper we introduce a new type of knowledge operator, called evidencebased knowledge, intended to capture the constructive core of common knowledge. An evidencebased knowledge system is obtained by augmenting a multiagent logic of knowledge with a system of evidence assertions t:ϕ (“t is an evidence for ϕ”) based on the following plausible assumptions: 1) each axiom has evidence; 3) evidence is checkable; 3) any evidence implies individual knowledge for each agent. Normally, the following monotonicity property is also assumed: 4) any piece of evidence is compatible with any other evidence. We show that the evidencebased knowledge operator is a stronger version of the common knowledge operator. Evidencebased knowledge is free of logical omniscience, modelindependent, and has a natural motivation. Furthermore, evidencebased knowledge can be presented by normal multimodal logics, which are in the scope of welldeveloped machinery applicable to modal logic: epistemic models, normalized proofs, automated proof search, etc. 1
The Logic of Justification
 Cornell University
, 2008
"... We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles origin ..."
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Cited by 30 (4 self)
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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the wellknown Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidencebased foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanKripke ‘Red Barn ’ paradox and analyze Russell’s ‘prime minister example ’ in Justification Logic. Furthermore, we formalize the wellknown Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. 1
Provability logic
 Handbook of Philosophical Logic, 2nd ed
, 2004
"... We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles origin ..."
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Cited by 25 (9 self)
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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the wellknown Justified True Belief vs. Knowledge problem. As a case study, we formalize Gettier examples in Justification Logic and reveal hidden assumptions and redundancies in Gettier reasoning. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidencebased foundation for epistemic logic. 1
Symmetric Logic of Proofs
 CUNY Ph.D. Program in Computer Science
, 2007
"... The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant an ..."
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Cited by 21 (9 self)
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The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant and hence not present in LP. For example, the choice function ‘+ ’ in LP, which is specified by the condition s:F ∨t:F → (s+t):F, is not necessarily symmetric. In this paper, we introduce an extension of the Logic of Proofs, SLP, which incorporates natural properties of the standard proof predicate in Peano Arithmetic: t is a code of a derivation containing F, including the symmetry of Choice. We show that SLP produces BrouwerHeytingKolmogorov proofs with a rich structure, which can be useful for applications in epistemic logic and other areas. 1
On Epistemic Logic with Justification
 NATIONAL UNIVERSITY OF SINGAPORE
, 2005
"... The true belief components of Plato's tripartite definition of knowledge as justified true belief are represented in formal epistemology by modal logic and its possible worlds semantics. At the same time, the justification component of Plato's definition did not have a formal representation. This ..."
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Cited by 20 (7 self)
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The true belief components of Plato's tripartite definition of knowledge as justified true belief are represented in formal epistemology by modal logic and its possible worlds semantics. At the same time, the justification component of Plato's definition did not have a formal representation. This
A note on some explicit modal logics
, 2006
"... Abstract. Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: “t is a possible justification of φ”. Motivated, in part, by this epistemic reading, Fitting introduced a Kripke style semantics for LP in [8]. In this note, w ..."
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Cited by 16 (0 self)
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Abstract. Artemov introduced the Logic of Proofs (LP) as a logic of explicit proofs. We can also offer an epistemic reading of this formula: “t is a possible justification of φ”. Motivated, in part, by this epistemic reading, Fitting introduced a Kripke style semantics for LP in [8]. In this note, we prove soundness and completeness of some axiom systems which are not covered in [8]. 1
Logical Omniscience as a Computational Complexity Problem
, 2009
"... The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge o ..."
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Cited by 16 (7 self)
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The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F.
On the complexity of the reflected logic of proofs
 Theoretical Computer Science
"... disjunctive property, complexity. Artemov’s system LP captures all propositional invariant properties of a proof predicate “x proves y ” ([1, 3]). Kuznets in [5] showed that the satisfiability problem for LP belongs to the class Π p 2 of the polynomial hierarchy. No nontrivial lower complexity bound ..."
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Cited by 14 (1 self)
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disjunctive property, complexity. Artemov’s system LP captures all propositional invariant properties of a proof predicate “x proves y ” ([1, 3]). Kuznets in [5] showed that the satisfiability problem for LP belongs to the class Π p 2 of the polynomial hierarchy. No nontrivial lower complexity bound for LP is known. We describe quite expressive syntactical fragment of LP which belongs to NP. It is rLP∧, ∨ – the set of all theorems of LP which are monotone boolean combinations of quasiatomic formulas (facts of sort “t proves F ”). A new decision algorithm for this fragment is proposed. It is based on a new simple independent formalization for rLP (the reflected fragment of LP) and involves the corresponding proof search procedure. Essentially rLP contains all the theorems of LP supplied with additional information about their proofs. We show that in many respects rLP is simpler than LP itself. This gives the complexity bound (NP) for rLP. In addition we prove a suitable variant of the disjunctive property which extends this bound to rLP∧,∨. 1 1
Semantics and tableaus for LPS4
 CUNY Ph.D. Program in Computer Science
, 2004
"... web page: comet.lehman.cuny.edu/fitting ..."