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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 31 (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 26 (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
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.
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 representat ..."
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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
 Proceedings of the Fifth Panhellenic Logic Symposium
, 2005
"... 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
Making Knowledge Explicit: How Hard It Is
, 2005
"... Artemov’s logic of proofs LP is a complete calculus of propositions and proofs, which is now becoming a foundation for the evidencebased approach to reasoning about knowledge. Additional atoms in LP have form t: F, read as “t is a proof of F ” (or, more generally, as “t is an evidence for F”) for a ..."
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Cited by 13 (1 self)
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Artemov’s logic of proofs LP is a complete calculus of propositions and proofs, which is now becoming a foundation for the evidencebased approach to reasoning about knowledge. Additional atoms in LP have form t: F, read as “t is a proof of F ” (or, more generally, as “t is an evidence for F”) for an appropriate system of terms t called proof polynomials. In this paper, we answer two wellknown questions in this area. One of the main features of LP is its ability to realize modalities in any S4derivation by proof polynomials thus revealing a statement about explicit evidences encoded in that derivation. We show that the original Artemov’s algorithm of building such realizations can produce proof polynomials of exponential length in the size of the initial S4derivation. We modify the realization algorithm to produce proof polynomials of at most quadratic length. We also found a modal formula, any realization of which necessarily requires selfreferential constants of type c: A(c). This demonstrates that the evidencebased reasoning encoded by the modal logic S4 is inherently selfreferential.