Journal of Philosophical Logic

, Volume 31, Issue 4, pp 359–386

Modal Logic, Truth, and the Master Modality


  • Torben Braüner
    • Department of Computer ScienceRoskilde University

DOI: 10.1023/A:1019992820056

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


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
Download to read the full article text

Copyright information

© Kluwer Academic Publishers 2002