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Modal Logic, Truth, and the Master Modality

Torben Braüner
Journal of Philosophical Logic
Vol. 31, No. 4 (Aug., 2002), pp. 359-386
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226760
Page Count: 28
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Modal Logic, Truth, and the Master Modality
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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 socalled 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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