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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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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
Referential logic of proofs
 Theoretical Computer Science
"... We introduce an extension of the propositional logic of singleconclusion proofs by the second order variables denoting the reference constructors of the type “the formula which is proved by x. ” The resulting Logic of Proofs with References, FLPref, is shown to be decidable, and to enjoy soundness ..."
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We introduce an extension of the propositional logic of singleconclusion proofs by the second order variables denoting the reference constructors of the type “the formula which is proved by x. ” The resulting Logic of Proofs with References, FLPref, is shown to be decidable, and to enjoy soundness and completeness with respect to the intended provability semantics. We show that FLPref provides a complete test of admissibility of inference rules in a sound extension of arithmetic. Key words: proof theory, explicit modal logic, single conclusion logic of proofs, proof term, reference, unification, admissible inference rule. 1
Explicit Proofs in Formal Provability Logic
 Logical Foundations of Computer Science. International Symposium, LFCS 2007
"... In this paper we answer the question what implicit proof assertions in the provability logic GL can be realized by explicit proof terms. In particular we show that the fragment of GL which can be realized by generalized proof terms of GLA is exactly S4∩GL and equals the fragment that can be realized ..."
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In this paper we answer the question what implicit proof assertions in the provability logic GL can be realized by explicit proof terms. In particular we show that the fragment of GL which can be realized by generalized proof terms of GLA is exactly S4∩GL and equals the fragment that can be realized by proofterms of LP. Additionally we show that the problem of determining which implicit provability assertions in a given modal formula can be made explicit is decidable. In the final sections of this paper we establish the disjunction property for GLA and give an axiomatization for GL ∩ S4. 1
Logic of knowledge with justifications from the
, 2004
"... provability perspective. ..."
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Basic systems of epistemic logic with justification
, 2005
"... An issue of an epistemic logic with justification has been discussed since the early 1990s. Such a logic, along with the usual knowledge operator ✷F (F is known), should contain assertions t:F (t is a justification for F), which gives a more nuanced and realistic model of knowledge. In this paper, w ..."
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An issue of an epistemic logic with justification has been discussed since the early 1990s. Such a logic, along with the usual knowledge operator ✷F (F is known), should contain assertions t:F (t is a justification for F), which gives a more nuanced and realistic model of knowledge. In this paper, we build two systems of epistemic logic with justification: the minimal one—S4LP—which is an extension of the basic epistemic logic S4 by an appropriate calculus of justification corresponding to the logic of proofs LP, and S4LPN—which is S4LP augmented by the explicit negative introspection principle ¬(t:F) → ✷¬(t:F). Epistemic semantics for both systems are suggested. Completeness and specific properties of S4LP and S4LPN, reflecting the explicit character of those systems, are established. 1
Russian Math. Surveys 59:2 203–229 c○2004 RAS(DoM) and LMS Uspekhi Mat. Nauk 59:2 9–36 DOI 10.1070/RM2004v059n02ABEH000715 Kolmogorov and Gödel’s approach to
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