Modal Logic, Truth, and the Master Modality
- Torben Braüner
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In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a so-called master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show that if attention is restricted to bidirectional frames, then the expressive power of the master modality is exactly what is needed to translate the bounded fragment of first-order logic into hybrid logic in a truth preserving way. We believe that this throws new light on Arthur Prior's fourth grade tense logic.
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- Modal Logic, Truth, and the Master Modality
Journal of Philosophical Logic
Volume 31, Issue 4 , pp 359-386
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- homophonic theories of truth
- hybrid logic
- modal logic
- Torben Braüner (1)
- Author Affiliations
- 1. Department of Computer Science, Roskilde University, P.O. Box 260, DK-4000, Roskilde, Denmark