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 -