Towards a Reasoning Model for Context-aware Systems: Modal Logic and the Tree Model Property

Abstract

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.

Depth-First Reasoning on Trees

“…The propositional µ-calculus is a modal logic with least and fixed-point operators, expressively corresponding to the monadic second order logic MSO [9]. This logic is known to subsume many temporal, program and description logics such as Preliminary results were presented in [11,12] the Linear Temporal Logic LTL, the Propositional Dynamic Logic PDL, the Computation Tree Logic CTL and ALC reg , which is an expressive description logic with negation and regular roles [4]. Due to its expressive power and nice computational properties, the µ-calculus has been extensively used as a reasoning framework in a wide range of domains, such as program verification, knowledge representation and concurrent pervasive systems [4].…”