Interval temporal logic plays a critical role in various applications, including planning, scheduling, and formal verification; recently, interval temporal logic has also been successfully applied to learning from temporal data. Halpern and Shoham’s interval temporal logic, in particular, stands out as a very intuitive, yet expressive, interval-based formalism. To address real-world scenarios involving uncertainty and imprecision, Halpern and Shoham’s logic has been recently generalized to the fuzzy (many-valued) case. The resulting language capitalizes on many-valued modal logics, allowing for a range of truth values that reflect multiple expert perspectives, but inherits the bad computational behaviour of its crisp counterpart. In this work, we investigate a sound and complete tableau system for fuzzy Halpern and Shoham’s logic, which, although possibly non-terminating, offers a semi-decision procedure for the finite case. 2012 ACM Subject Classification Theory of computation → Theory and algorithms for application domains
Conradie, W., Monego, R., Munoz-Velasco, E., Sciavicco, G., Stan, I. (2023). A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic. In 30th International Symposium on Temporal Representation and Reasoning, TIME 2023. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing [10.4230/LIPIcs.TIME.2023.9].
A Sound and Complete Tableau System for Fuzzy Halpern and Shoham’s Interval Temporal Logic
Stan I. E.
2023
Abstract
Interval temporal logic plays a critical role in various applications, including planning, scheduling, and formal verification; recently, interval temporal logic has also been successfully applied to learning from temporal data. Halpern and Shoham’s interval temporal logic, in particular, stands out as a very intuitive, yet expressive, interval-based formalism. To address real-world scenarios involving uncertainty and imprecision, Halpern and Shoham’s logic has been recently generalized to the fuzzy (many-valued) case. The resulting language capitalizes on many-valued modal logics, allowing for a range of truth values that reflect multiple expert perspectives, but inherits the bad computational behaviour of its crisp counterpart. In this work, we investigate a sound and complete tableau system for fuzzy Halpern and Shoham’s logic, which, although possibly non-terminating, offers a semi-decision procedure for the finite case. 2012 ACM Subject Classification Theory of computation → Theory and algorithms for application domains
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