Modal Logic, Truth, and the Master Modality
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.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngJournal of Philosophical LogicSpringer Journalshttp://www.deepdyve.com/lp/springer-journals/modal-logic-truth-and-the-master-modality-rrhallvCPn