Contextual Validity in Hybrid Logic

Hybrid tense logic is an extension of Priorean tense logic in which it is possible to refer to times using special propositional sym- bols called nominals. Temporal indexicals are expressions such as now, yesterday, today, tomorrow and four days ago that have highly context- dependent interpretations. Moreover, such indexicals give rise to a special kind of validity—contextual validity—that interacts with ordinary logi- cal validity in interesting and often unexpected ways. In this paper we model these interactions by combining standard techniques from hybrid logic with insights from the work of Hans Kamp and David Kaplan. We introduce a simple proof rule, which we call the Kamp Rule, and first we show that it is all we need to take us from logical validities involving now to contextual validities involving now too. We then go on to show that this deductive bridge is strong enough to carry us to contextual validities involving yesterday, today and tomorrow as well.