Elsevier

Journal of Applied Logic

Volume 8, Issue 4, December 2010, Pages 356-370
Journal of Applied Logic

Justification logics and hybrid logics

https://doi.org/10.1016/j.jal.2010.08.007Get rights and content
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Abstract

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.

Keywords

Hybrid logic
Justification logic
Logic of proofs
Nominals

Cited by (0)

This research was supported by NSF grant 0830450.