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.