A finite basis for 'almost future' temporal logic over the reals

Dorit Pardo*, Alexander Rabinovich

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

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. In this paper we show that finiteness can be recovered if we slightly soften the requirement that future formulas must be totally past-independent: We allow formulas to depend just on the very very near-past, and maintain the requirement that they be independent of the rest - actually - of most of the past. We call them 'almost future' formulas, and show that there is a finite basis of almost future modalities which is expressively complete over the Reals for the almost future fragment of FOMLO.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2012 - 37th International Symposium, MFCS 2012, Proceedings
Pages740-751
Number of pages12
DOIs
StatePublished - 2012
Event37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012 - Bratislava, Slovakia
Duration: 27 Aug 201231 Aug 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7464 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012
Country/TerritorySlovakia
CityBratislava
Period27/08/1231/08/12

Fingerprint

Dive into the research topics of 'A finite basis for 'almost future' temporal logic over the reals'. Together they form a unique fingerprint.

Cite this