TY - GEN

T1 - Decidability and expressive power of real time logics

AU - Rabinovich, Alexander

PY - 2006

Y1 - 2006

N2 - Temporal Logic based on the two modalities "Since" and "Until" (TL) is popular among computer scientists as the framework for reasoning about a system evolving in time. This logic is usually referred to as the standard linear time temporal logic. The "linear time" appears in the name of this logic probably because when it was introduced by Pnueli its intended models were linear orders; more precisely, ω-models. The adjective "standard" is presumable used due to the Kamp theorem which states that it is expressively equivalent (over the w-models) to first order monadic logic of order - a very fundamental logic. The two logics are expressively equivalent whether the system evolves in discrete steps or in continuous time; however, for continuous time, both logics can not express properties like: "X will happen exactly after one unit of time." Unfortunately, the extension of TL by this modality is undecidable. Two of the most important characteristics of specification formalisms are expressive power and the decidability/complexity of the validity and model checking problems. Over the years, different extensions of TL which can specify metric properties of real time were suggested. The goal of this talk is to survey expressiveness and decidability results for temporal and predicate logics for the specification of metric properties of real time.

AB - Temporal Logic based on the two modalities "Since" and "Until" (TL) is popular among computer scientists as the framework for reasoning about a system evolving in time. This logic is usually referred to as the standard linear time temporal logic. The "linear time" appears in the name of this logic probably because when it was introduced by Pnueli its intended models were linear orders; more precisely, ω-models. The adjective "standard" is presumable used due to the Kamp theorem which states that it is expressively equivalent (over the w-models) to first order monadic logic of order - a very fundamental logic. The two logics are expressively equivalent whether the system evolves in discrete steps or in continuous time; however, for continuous time, both logics can not express properties like: "X will happen exactly after one unit of time." Unfortunately, the extension of TL by this modality is undecidable. Two of the most important characteristics of specification formalisms are expressive power and the decidability/complexity of the validity and model checking problems. Over the years, different extensions of TL which can specify metric properties of real time were suggested. The goal of this talk is to survey expressiveness and decidability results for temporal and predicate logics for the specification of metric properties of real time.

UR - http://www.scopus.com/inward/record.url?scp=33750346664&partnerID=8YFLogxK

U2 - 10.1007/11867340_3

DO - 10.1007/11867340_3

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AN - SCOPUS:33750346664

SN - 3540450262

SN - 9783540450269

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 32

BT - Formal Modeling and Analysis of Timed Systems - 4th International Conference, FORMATS 2006, Proceedings

PB - Springer Verlag

Y2 - 25 September 2006 through 27 September 2006

ER -