Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
Logic in Computer Science
2019-03-14 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0706.0692,
title = {Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems},
author = {Dimitar P. Guelev},
journal= {arXiv preprint arXiv:0706.0692},
year = {2019}
}