A Substructural Approach to Explicit Modal Logic

This paper will develop ideas from [44]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a proof of the internalization theorem. Second, we provide alternative frames that more closely resemble the standard versions of the ternary relational frames, as well as a more general approach to the completeness proof. We prove that soundness and completeness hold for justification logics over a wide variety of base logics. Finally, we will strengthen Belnap’s variable sharing for the justification logic context, demonstrating that the justifications are properly relevant justifications.

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A Substructural Approach to Explicit Modal Logic

Cited by 2 publications

References 47 publications

Getting some (non-classical) closure with justification logic

Getting some (non-classical) closure with justification logic

Weak relevant justification logics

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