TY - GEN
T1 - On almost future temporal logics
AU - Rabinovich, Alexander
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
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. 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.
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. 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.
UR - http://www.scopus.com/inward/record.url?scp=84951870362&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-23534-9_16
DO - 10.1007/978-3-319-23534-9_16
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84951870362
SN - 9783319235332
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 261
EP - 272
BT - Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday
A2 - Blass, Andreas
A2 - Finkbeiner, Bernd
A2 - Dershowitz, Nachum
A2 - Schulte, Wolfram
A2 - Beklemishev, Lev D.
PB - Springer Verlag
T2 - Symposium on Yurifest, 2015
Y2 - 11 September 2015 through 12 September 2015
ER -