A Sound and Complete Tableau System for Fuzzy Halpern and Shoham's Interval Temporal Logic

Willem Conradie, Riccardo Monego, Emilio Muñoz-Velasco, Guido Sciavicco, Ionel Eduard Stan

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.