Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
نویسندگان
چکیده
منابع مشابه
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC ) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect ...
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This paper introduces infinite intervals into the Duration Calculus [32]. The extended calculus defines a state duration over an infinite interval by a property which specifies the limit of the state duration over finite intervals, and excludes the description operator. Thus the calculus can be established without involvement of unpleasant calculation of infinity. With limits of state durations...
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Di erent interval modal logics have been proposed for reasoning about the temporal behaviour of digital systems. Some of them are purely propositional and only enable the speci cation of qualitative time requirements. Others, such as ITL and the duration calculus, are rst order logics which support the expression of quantitative, real-time requirements. These two logics have in common the prese...
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Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonte...
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This paper presents an ω-complete proof system for the extension of first order Interval Temporal Logic (ITL, [12, 15, 4]) by a projection operator [16, 11]. Alternative earlier approaches to the axiomatisation of projection in ITL are briefly presented and discussed. An extension of the proof system which is complete for the extension of Duration Calculus (DC , [24]) by projection is also given.
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2007
ISSN: 1860-5974
DOI: 10.2168/lmcs-3(3:3)2007