TY - JOUR
T1 - Monadic logic of order over naturals has no finite base
AU - Beauquier, Danièle
AU - Rabinovich, Alexander
PY - 2002/4
Y1 - 2002/4
N2 - A major result concerning Temporal Logics (TL) is Kamp's theorem which states that the temporal logic over the pair of modalities X until Y and X since Y is expressively complete for the first-order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have the same expressive power over the natural numbers. As a consequence of our proof, we obtain that there is no finite base temporal logic which is expressively complete for the μ-calculus.
AB - A major result concerning Temporal Logics (TL) is Kamp's theorem which states that the temporal logic over the pair of modalities X until Y and X since Y is expressively complete for the first-order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have the same expressive power over the natural numbers. As a consequence of our proof, we obtain that there is no finite base temporal logic which is expressively complete for the μ-calculus.
KW - Monadic logics
KW - Temporal logics
UR - http://www.scopus.com/inward/record.url?scp=0036538802&partnerID=8YFLogxK
U2 - 10.1093/logcom/12.2.243
DO - 10.1093/logcom/12.2.243
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AN - SCOPUS:0036538802
SN - 0955-792X
VL - 12
SP - 243
EP - 253
JO - Journal of Logic and Computation
JF - Journal of Logic and Computation
IS - 2
ER -