FALL 2004
Tuesday, 2pm – 4pm, room TBA
September 7 meeting
Sergei Artemov will speak on “Provability approach to logics of knowledge with justifications”
a joint work with Elena Nogina
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 operator “F is known” should contain assertions “t is an evidence of F”. In this paper we build a logic of knowledge with justifications, 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 necessary principles connecting knowledge and justifications. We offer a provability semantics for LPS4 where the epistemic modality K(F) is interpreted as “F is true and provable” and the evidence assertions as “t is a proof of F”. We establish decidability and Kripke completeness of LPS4. On the way to LPS4 we find the minimal joint logic of proofs and formal provability, LPGL complete with respect to the standard provability semantics.
There will be a discussion about new open problems immediately available for exploration.