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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 52 (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 44 (5 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 44 (14 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
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 26 (9 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
Fluctuations, effective learnability and metastability in analysis
"... This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the lawofexcludedmiddle, one can extract functionals (B, L), where L is a learning proced ..."
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Cited by 6 (1 self)
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This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the lawofexcludedmiddle, one can extract functionals (B, L), where L is a learning procedure for a rate of convergence which succeeds after at most B(a)many mind changes. This (B, L)learnability provides quantitative information strictly in between a full rate of convergence (obtainable in general only from semiconstructive proofs) and a rate of metastability in the sense of Tao (extractable also from classical proofs). In fact, it corresponds to rates of metastability of a particular simple form. Moreover, if a certain gap condition is satisfied, then B and L yield a bound on the number of possible fluctuations. We explain recent applications of proof mining to ergodic theory in terms of these results.
Justification logics and hybrid logics
 Journal of Applied Logic
, 2010
"... Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the mod ..."
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Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less wellknown than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here. 1
Data Storage Interpretation of Labeled Modal Logic
"... We introduce reference structures  a basic mathematical model of a data organization capable to store and utilize information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for m ..."
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Cited by 3 (2 self)
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We introduce reference structures  a basic mathematical model of a data organization capable to store and utilize information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming languages is presented as an example of a reference structure building. 1 Introduction We suggest to interpret a labeled modal formula [[m]]A as "memory cell m stores sentence A" and to treat propositional variables as names of the cell contents. The Annals of Pure and Applied Logic, v. 78, pp. 5771, 1996 y The research described in this publication was made possible in part by Grant No.NFQ...
Logic of Proofs with the strong provability operator
 University of Amsterdam
, 1994
"... Logics with the strong provability operator ": : : is true and provable" together with the proof operators "p is a proof of : : :" are axiomatized. Kripkestyle completeness, decidability and arithmetical completeness of these logics are established. 1 Introduction Logics with th ..."
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Logics with the strong provability operator ": : : is true and provable" together with the proof operators "p is a proof of : : :" are axiomatized. Kripkestyle completeness, decidability and arithmetical completeness of these logics are established. 1 Introduction Logics with the provability operator ": : : is provable" and the proof operators "p is a proof of : : :" corresponding to certain natural classes of proof predicates in Peano arithmetic PA were introduced in [1]. In some respect (see e.g. [2],[3]) the strong provability operator ": : : is true and provable" provides a better model for provability than the operator ": : : is provable". The logic of the strong provability operator is known ([4]) to coincide with Grzegorczyk logic Grz. In this paper we present joint logics with both the strong provability operator and the proof operators. These logics are proved to be decidable; natural Research supported by the grant No. 2.1.21 of the Program "Universities of Russia"and ...
Logic of Proofs for bounded arithmetic
, 2005
"... The logic of proofs is known to be complete for the semantics of proofs in PA. In this paper we present a refinement of this theorem, we will show that we can assure that all the operations on proofs can be realized by feasible, that is PTIMEcomputable, functions. In particular we will show that th ..."
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The logic of proofs is known to be complete for the semantics of proofs in PA. In this paper we present a refinement of this theorem, we will show that we can assure that all the operations on proofs can be realized by feasible, that is PTIMEcomputable, functions. In particular we will show that the logic of proofs is complete for the semantics of proofs in Buss’ bounded arithmetic S 1 2. 1