Finite-trace linear temporal logic: coinductive completeness

Linear temporal logic (LTL) is suitable not only for infinite-trace systems, but also for finite-trace systems. In particular, LTL with finite-trace semantics is frequently used as a specification formalism in runtime verification, in artificial intelligence, and in business process modeling. The sa...

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Vydané v:	Formal methods in system design Ročník 53; číslo 1; s. 138 - 163
Hlavný autor:	Roşu, Grigore
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.08.2018 Springer Nature B.V
Predmet:	Axioms CAE) and Design Circuits and Systems Computer-Aided Engineering (CAD Decision theory Electrical Engineering Engineering Semantics Software Engineering/Programming and Operating Systems Temporal logic Coinduction Complete deduction Linear temporal logic Satisfiability
ISSN:	0925-9856, 1572-8102
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Abstract	Linear temporal logic (LTL) is suitable not only for infinite-trace systems, but also for finite-trace systems. In particular, LTL with finite-trace semantics is frequently used as a specification formalism in runtime verification, in artificial intelligence, and in business process modeling. The satisfiability of LTL with finite-trace semantics, a known PSPACE-complete problem, has been recently studied and both indirect and direct decision procedures have been proposed. However, the proof theory of LTL with finite traces is not that well understood. Specifically, complete proof systems of LTL with only infinite or with both infinite and finite traces have been proposed in the literature, but complete proof systems directly for LTL with only finite traces are missing. The only known results are indirect, by translation to other logics, e.g., infinite-trace LTL. This paper proposes a direct sound and complete proof system for finite-trace LTL. The axioms and proof rules are natural and expected, except for one rule of coinductive nature, reminiscent of the Gödel–Löb axiom.
AbstractList	Linear temporal logic (LTL) is suitable not only for infinite-trace systems, but also for finite-trace systems. In particular, LTL with finite-trace semantics is frequently used as a specification formalism in runtime verification, in artificial intelligence, and in business process modeling. The satisfiability of LTL with finite-trace semantics, a known PSPACE-complete problem, has been recently studied and both indirect and direct decision procedures have been proposed. However, the proof theory of LTL with finite traces is not that well understood. Specifically, complete proof systems of LTL with only infinite or with both infinite and finite traces have been proposed in the literature, but complete proof systems directly for LTL with only finite traces are missing. The only known results are indirect, by translation to other logics, e.g., infinite-trace LTL. This paper proposes a direct sound and complete proof system for finite-trace LTL. The axioms and proof rules are natural and expected, except for one rule of coinductive nature, reminiscent of the Gödel–Löb axiom.
Author	Roşu, Grigore
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Snippet	Linear temporal logic (LTL) is suitable not only for infinite-trace systems, but also for finite-trace systems. In particular, LTL with finite-trace semantics...
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SubjectTerms	Axioms CAE) and Design Circuits and Systems Computer-Aided Engineering (CAD Decision theory Electrical Engineering Engineering Semantics Software Engineering/Programming and Operating Systems Temporal logic
Title	Finite-trace linear temporal logic: coinductive completeness
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