TY - JOUR
T1 - Temporal logics with incommensurable distances are undecidable
AU - Rabinovich, Alexander
PY - 2007/5
Y1 - 2007/5
N2 - Temporal logic based on the two modalities "Since" and "Until" (TL) is the most popular logic for the specification of reactive systems. It is often called the linear time temporal logic. However, metric properties of real time cannot be expressed in this logic. The simplest modalities with metric properties are "Xwill happen within δ units of time". The extension of TL by all these modalities with rational S is decidable. We show that the extension of the linear time temporal logic by two modalities "Xwill happen within one unit of time", "X will happen within τ unit of time" is undecidable, whenever τ is irrational.
AB - Temporal logic based on the two modalities "Since" and "Until" (TL) is the most popular logic for the specification of reactive systems. It is often called the linear time temporal logic. However, metric properties of real time cannot be expressed in this logic. The simplest modalities with metric properties are "Xwill happen within δ units of time". The extension of TL by all these modalities with rational S is decidable. We show that the extension of the linear time temporal logic by two modalities "Xwill happen within one unit of time", "X will happen within τ unit of time" is undecidable, whenever τ is irrational.
UR - http://www.scopus.com/inward/record.url?scp=84855199630&partnerID=8YFLogxK
U2 - 10.1016/j.ic.2006.11.002
DO - 10.1016/j.ic.2006.11.002
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AN - SCOPUS:84855199630
VL - 205
SP - 707
EP - 715
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
IS - 5
ER -