TY - GEN
T1 - A finite basis for 'almost future' temporal logic over the reals
AU - Pardo, Dorit
AU - Rabinovich, Alexander
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84864988022&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-32589-2_64
DO - 10.1007/978-3-642-32589-2_64
M3 - منشور من مؤتمر
SN - 9783642325885
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 740
EP - 751
BT - Mathematical Foundations of Computer Science 2012 - 37th International Symposium, MFCS 2012, Proceedings
T2 - 37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012
Y2 - 27 August 2012 through 31 August 2012
ER -