TR-2005004: Basic Systems of Epistemic Logic with Justification
Sergei Nikolaevich Artemov, Elena Nogina · CUNY Academic Works (City University of New York) · 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 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 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 ) → 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.