Journal of Philosophical Logic

, Volume 31, Issue 4, pp 359–386

Modal Logic, Truth, and the Master Modality

Authors

  • Torben Braüner
    • Department of Computer ScienceRoskilde University
Article

DOI: 10.1023/A:1019992820056

Cite this article as:
Braüner, T. Journal of Philosophical Logic (2002) 31: 359. doi:10.1023/A:1019992820056

Abstract

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.

homophonic theories of truthhybrid logicmodal logic
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© Kluwer Academic Publishers 2002