Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation

Many-valued logics, often referred to as fuzzy logics, are a fundamental tool for reasoning about uncertainty, and are based on truth value algebras that generalize the Boolean one; the same logic can be interpreted on algebras from different varieties, for different purposes and pose different challenges. Although temporal many-valued logics, that is, the many-valued counterpart of popular temporal logics, have received little attention in the literature, the many-valued generalization of Halpern and Shoham’s interval temporal logic has been recently introduced and studied, and a sound and complete tableau system for it has been presented for the case in which it is interpreted on some finite Heyting algebra. In this paper, we take a step further in this inquiry by exploring a tableau system for Halpern and Shoham’s interval temporal logic interpreted on some finite FL\(_{ew}\)-algebra, therefore generalizing the Heyting case, and by providing its open-source implementation.

Recommended citation: Badia, Guillermo, Noguera, Carles, Paparella, Alberto, Sciavicco, Guido, and Stan, Eduard I. (2024). "Fitting's Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation." 31st International Symposium on Temporal Representation and Reasoning (TIME 2024), Montpellier, France, 28-30 October 2024. 1(1).
Download Paper