David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
Dov M. Gabbay, Ian Hodkinson & Mark Reynolds (1994). Temporal Logic Mathematical Foundations and Computational Aspects. Monograph Collection (Matt - Pseudo).
George Gargov & Valentin Goranko (1993). Modal Logic with Names. Journal of Philosophical Logic 22 (6):607 - 636.
Brian F. Chellas (1992). Time and Modality in the Logic of Agency. Studia Logica 51 (3-4):485 - 517.
Dov M. Gabbay (1981). An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames. In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht 67--89.
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.
Alberto Zanardo (2006). Quantification Over Sets of Possible Worlds in Branching-Time Semantics. Studia Logica 82 (3):379 - 400.
Max A. Freund (2007). A Two Dimensional Tense-Modal Sortal Logic. Journal of Philosophical Logic 36 (5):571 - 598.
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