Modal logics forms a family of formalisms widely used as reasoning frameworks in diverse areas of computer science. Description logics and their application to the web semantic is a notable example. Also, description logics have been recently used as a reasoning model for context-aware systems. Most reasoning algorithms for modal (description) logics are based on tableau constructions. In this work, we propose a reasoning (satisfiability) algorithm for the multi-modal Km with converse. The algorithm is based on the finite tree model property and a Fischer-Ladner construction. We show the algorithm is sound and complete, and we provide the corresponding complexity analysis. We also present some exploratory results of a preliminary implementation of the algorithm.
Context-aware systems are ubiquitous computing systems capable to adapt their behavior according to a dynamical changing environment. The development of reasoning and modeling techniques of context information have resulted a challenging task due to the inherent complexity of dynamical systems. In particular, modeling time and location context information have been so far constrained in current formalisms for context-aware computing due to expressive and computational limitations. Due to the well-known balance of expressive power and efficient reasoning algorithms associated to modal logics, we propose in the current work the use of expressive modal logics as a reasoning framework for context-aware pervasive systems. In particular, we describe a consistency model for a context-aware communication system. The consistency of this model is characterized in term of the satisfiability of the µ-calculus (an expressive modal logic).
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