A propositional logic of temporal connectives

Richard L. Epstein, Esperanza Buitrago-Díaz

DOI: http://dx.doi.org/10.12775/LLP.2014.020

Abstract


We investigate how to formalize reasoning that takes account of time by using connectives like “before” and “after.” We develop semantics for a formal logic, which we axiomatize. In proving that the axiomatization is strongly complete we show how a temporal ordering of propositions can yield a linear timeline. We formalize examples of ordinary language sentences to illustrate the scope and limitations of this method. We then discuss ways to deal with some of those limitations.

Keywords


temporal logic; propositional logic; completeness theorem; linear orderings; subjective experience of time

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References


Allen, J. F., “Maintaining knowledge about temporal intervals”, Communications of the ACM, 26, 11 (1983): 832–843. DOI: 10.1145/182.358434

Epstein, R. L., Propositional Logics (The Semantic Foundations of Logic) Kluwer, 1990. 2nd edition, Oxford University Press, 1995. 2nd edition with corrections, Wadsworth, 2000. 3rd edition, Advanced Reasoning Forum, 2012.

Epstein, R. L., “Truth and reasoning”, pages 101–127 in Prescriptive Reasoning, Advanced Reasoning Forum.

Epstein, R. L., “Reflections on temporal and modal logic”, Logic and Logical Philosophy (2014). DOI: 10.12775/LLP.2014.015

Epstein, R. L., Logic, Language, and the World, vol. 2 “Time and Space”. Advanced Reasoning Forum (previously available as part of a draft called “The Internal Structure of Predicates and Names with an Analysis of Reasoning about Process” at http://www.AdvancedReasoningForum.org.

Epstein, R. L., and Walter A. Carnielli, Computability, Wadsworth & Brooks/Cole/ 1989. 3rd edition, Advanced Reasoning Forum, 2008.








Print ISSN: 1425-3305
Online ISSN: 2300-9802

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