Justification logics and hybrid logics

Hybrid logics internalize their own semantics. Members of the newer family of justification logics internalize their own proof methodology. It is an appealing goal to combine these two ideas into a single system, and in this paper we make a start. We present a hybrid/justification version of the modal logic T. We give a semantics, a proof theory, and prove a completeness theorem. In addition, we prove a Realization Theorem, something that plays a central role for justification logics generally. Since justification logics are newer and less well-known than hybrid logics, we sketch their background, and give pointers to their range of applicability. We conclude with suggestions for future research. Indeed, the main goal of this paper is to encourage others to continue the investigation begun here.

• Type: Journal
• Year: 2010
• Where: JAPLL
• Authors: Melvin Fitting
• Keywords: Hybrid Logics, JAPLL 2010, Justification Logics, Logics