 
Summary: Basic systems of epistemic logic with justification
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
February 21, 2005
Abstract
An issue of an epistemic logic with justification 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 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 oneS4LPwhich is an extension of the basic epistemic logic S4
by an appropriate calculus of justification corresponding to the logic of
proofs LP, and S4LPNwhich is S4LP augmented by the explicit negative
introspection principle ¬(t:F) 2¬(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.
