Basic systems of epistemic logic with justification
Sergei Nikolaevich Artemov, Elena Nogina · 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, 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