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Reflections on temporal and modal logic

100%
Epstein R. L.
Logic and Logical Philosophy
|
2015
|
vol. 24
|
issue 1
111–139
EN
The most popular method of incorporating time into a formal logic is based on the work of Arthur Prior. It treats tenses as operators on sentences. In this essay I show a serious problem with that approach, a confusion of scheme versus proposition, which makes any system built in that way incoherent. I will compare how other formal logics deal with the scheme versus proposition distinction and find that only for formal modal logics does the same problem arise. I then compare Prior’s approach to other ways of taking time into account in formal logics.
2

A propositional logic of temporal connectives

63%
Epstein R. L., Buitrago-Díaz E.
Logic and Logical Philosophy
|
2015
|
vol. 24
|
issue 2
155–200
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.
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