TY - JOUR
T1 - Future temporal logic needs infinitely many modalities
AU - Hirshfeld, Yoram
AU - Rabinovich, Alexander
PY - 2003/12/15
Y1 - 2003/12/15
N2 - Kamp's theorem states that there is a temporal logic with two modalities ("until" and "since") which is expressively complete for the first-order monadic logic of order over the real line. In this paper we show that there is no temporal logic with finitely many modalities which is expressively complete for the future fragment of first-order monadic logic of order over the real line (a future formula over the real time line is a formula whose truth value and a point is independent of what happened in the past).
AB - Kamp's theorem states that there is a temporal logic with two modalities ("until" and "since") which is expressively complete for the first-order monadic logic of order over the real line. In this paper we show that there is no temporal logic with finitely many modalities which is expressively complete for the future fragment of first-order monadic logic of order over the real line (a future formula over the real time line is a formula whose truth value and a point is independent of what happened in the past).
UR - https://www.scopus.com/pages/publications/0346335710
U2 - 10.1016/S0890-5401(03)00163-9
DO - 10.1016/S0890-5401(03)00163-9
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AN - SCOPUS:0346335710
SN - 0890-5401
VL - 187
SP - 196
EP - 208
JO - Information and Computation
JF - Information and Computation
IS - 2
ER -