Fuzzy-temporal approach to the handling of temporal interval relations and preferences

In this paper we propose a multi-valued extension of the Halpern-Shoham logic (HS). The HS system is a modal logic of time intervals, with a rich set of ordering relations between intervals, which is potentially useful for temporal planning issues. Our extension may be exploited for a representation of both temporal relations and preferences, which adds some "rationality' for this planning. The linearity relations of preferences (less or more preferable), when combined with time, often lose their sense, and become inapplicable. We intend to show the completeness of a preferential component of the system, w.r.t. the interval-based semantics and that its satisfiability property belong to the class of PSPACE problems.