Contextual Validity in Hybrid Logic

Patrick Rowan Blackburn, Klaus Frovin Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

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
Original languageDanish
Title of host publicationModeling and using context : 8th International and Interdisciplinary Conference, CONTEXT 2013, Annecy, France, October 28 -31, 2013, Proceedings
EditorsPatrick Brezillion, Patrick Blackburn
Number of pages14
PublisherSpringer Publishing Company
Publication date2013
Pages185-198
Publication statusPublished - 2013
SeriesLecture Notes in Computer Science
Volume8175
ISSN0302-9743

Cite this

Blackburn, P. R., & Jørgensen, K. F. (2013). Contextual Validity in Hybrid Logic. In P. Brezillion, & P. Blackburn (Eds.), Modeling and using context: 8th International and Interdisciplinary Conference, CONTEXT 2013, Annecy, France, October 28 -31, 2013, Proceedings (pp. 185-198). Springer Publishing Company. Lecture Notes in Computer Science, Vol.. 8175