Efficient decision procedure for Belief modality

Abstract

This paper defines decision algorithm for subclass of B^KD45D^KDI^KD logic which is based on known algorithm for temporal B^KD45D^KDI^KD logic [2]. BDI logics are widely used in agent based systems. Such usage of BDI logic can be found in [1]. The original decision algorithm uses loop-check technique for BEL and temporal operators. Applied loop-check technique is not optimized and therefore loop-check takes most of the time used in decision algorithm. Some examples of efficient loop-check applications for logic KT, S4 and some subclasses of intuitionistic logic can be found in [4]. Another efficient loop-check can be found in work [3]. We concentrate on our attitude on loop-check optimization for BEL operator. This paper defines decision algorithm modification, which uses efficient loop-check for BEL operator, but do not effect performance of other parts of algorithm. We define optimization only for BEL operator and therefore we omit temporal operators in this paper.