Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

Details Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

2007-06-05

arxiv.org/abs/0706.0692v2

LMCS 3 (3:3) 2007

Computer Science

Logic in Computer Science

43 pages

Scientific paper

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 to real-time semantics. The proposed systems subsume probabilistic real-time DC as known from the literature. A correspondence between the proposed systems and a system of probabilistic interval temporal logic with finite intervals and expanding modalities is established too.

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