Hilbertian tense logic

Lecture 2 : Time , tense , and tense - logic ∗

Hilbertian Deductive Systems, Infon Logic, and Datalog

In the first part of the paper, we develop a general method for converting derivability problems, from a broad range of deductive systems, into the derivability problem in a quite specific system, namely the Datalog fragment of universal Horn logic. In this generality, the derivability problems may not be recursively solvable, let alone feasible; in particular, we may get Datalog “programs” wit...

Times in Tense Logic

Tense logic is often said to possess insufficient expressive resources to serve as a theory of the nature of time. This paper counters this objection by showing how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators “it was the case that” and “it will be the case that.” This account of tim...

Indexical Hybrid Tense Logic

In this paper we explore the logic of now, yesterday, today and tomorrow by combining the semantic approach to indexicality pioneered by Hans Kamp [9] and refined by David Kaplan [10] with hybrid tense logic. We first introduce a special now nominal (our @now corresponds to Kamp’s original now operator N) and prove completeness results for both logical and contextual validity. We then add propo...

Functional Completeness in Tense Logic

Consider a partially ordered set(T <,=), where T is non-empty,< is an irreflexive and transitive relation on T and = is equality. We can regard T as a set of moments of time and < as the earlier later relation. We refer to any fixed (T,<,=) as a flow of time. Consider now a propositional language with atomic propositions p, q, r, . . . the usual classical connectives ∼,∧,∨ → and some additional...