A propositional logic of temporal connectives

• Authors: Epstein Richard L. , Buitrago-Díaz Esperanza
• Languages of publication: EN

Abstracts

EN

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

EN

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

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 2
• Pages: 155–200

Dates

published

2015-06-01

online

2014-09-06

Contributors

author

Epstein Richard L.

• Advanced Reasoning Forum, Dogshine, New Mexico, USA

author

Buitrago-Díaz Esperanza

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.

Identifiers

DOI

10.12775/LLP.2014.020