Combinations of tense and modality for predicate logic

Journal of Philosophical Logic 28 (4):371-398 (1999)
In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T x W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T x Wsemantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed
Keywords tense  modality  Kamp-semantics  T×W-semantics  (strong) completeness
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DOI 10.1023/A:1004359325754
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References found in this work BETA
George Gargov & Valentin Goranko (1993). Modal Logic with Names. Journal of Philosophical Logic 22 (6):607 - 636.

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Citations of this work BETA
Thomas Müller (forthcoming). Time and Determinism. Journal of Philosophical Logic:1-12.
Stefan Wölfl (2002). Propositional Q-Logic. Journal of Philosophical Logic 31 (5):387-414.
Max A. Freund (2007). A Two Dimensional Tense-Modal Sortal Logic. Journal of Philosophical Logic 36 (5):571 - 598.

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