Indexical Hybrid Tense Logic
Patrick Blackburn, Klaus Frovin Jørgensen · RUCforsk (Roskilde University) · 2012
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 propositional constants to handle yesterday, today and tomorrow; our system correctly treats sentences like “Niels will die yesterday” as contextually unsatisfiable. Building on our completeness results for now, we prove completeness for the richer language, again for both logical and contextual validity.