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Logic of knowledge with justifications from the provability perspective.
 

Summary: Logic of knowledge with justifications
from the provability perspective.
Sergei Artemov Elena Nogina
Graduate Center CUNY BMCC CUNY
Ph.D. Program in Computer Science Department of Mathematics
365 Fifth Avenue 199 Chambers Street
New York, NY 10016, U.S.A. New York, NY 10007, U.S.A.
SArtemov@gc.cuny.edu ENogina@bmcc.cuny.edu
September 24, 2004
Abstract
An issue of a logic of knowledge with justifications has been discussed
since the early 1990s. Such a logic along with the usual knowledge oper-
ator 2F "F is known" should contain assertions t:F "t is an evidence of
F". In this paper we build two systems of logic of knowledge with justi-
fications: LPS4, which is an extension of the basic epistemic logic S4 by
an appropriate calculus of evidences corresponding to the logic of proofs
LP together with the principle that justification implies knowledge, and
LPS4-
, which is LPS4 augmented by the mixed implicit/explicit negative
introspection principle. We offer a provability semantics for LPS4 and

  

Source: Artemov, Sergei N. - Faculty of Mechanics and Mathematics, Moscow State University

 

Collections: Computer Technologies and Information Sciences