Blackburn, Patrick Rowan3; Jørgensen, Klaus Frovin4
Patrick Brezillion, Patrick Blackburn
1 Videnskabsstudier, Department of Communication and Arts, Roskilde University2 The Department of Culture and Identity, Roskilde University3 Department of Communication and Arts, Roskilde University4 Language and rationality, The Department of Culture and Identity, Roskilde University
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.
Lecture Notes in Computer Science: 8th International and Interdisciplinary Conference, Context 2013, Annecy, France, October 28 -31, 2013, Proceedings, 2013, p. 185-198