On almost future temporal logics

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Abstract

Kamp’s theorem established the expressive completeness of the temporal modalities Until and Since for the First-Order Monadic Logic of Order (FOMLO) over real and natural time flows. Over natural time, a single future modality (Until) is sufficient to express all future FOMLO formulas. These are formulas whose truth value at any moment is determined by what happens from that moment on. Yet this fails to extend to real time domains: here no finite basis of future modalities can express all future FOMLO formulas. Almost future formulas extend future formulas; they depend just on the very near past, and are independent of the rest of the past. For almost future formulas finiteness is recovered over Dedekind complete time flows. In this paper we show that there is no temporal logic with finitely many modalities which is expressively complete for the almost future fragment of FOMLO over all linear flows.

Original languageEnglish
Title of host publicationFields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday
EditorsAndreas Blass, Bernd Finkbeiner, Nachum Dershowitz, Wolfram Schulte, Lev D. Beklemishev
PublisherSpringer Verlag
Pages261-272
Number of pages12
ISBN (Print)9783319235332
DOIs
StatePublished - 2015
EventSymposium on Yurifest, 2015 - Berlin, Germany
Duration: 11 Sep 201512 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9300
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceSymposium on Yurifest, 2015
Country/TerritoryGermany
CityBerlin
Period11/09/1512/09/15

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