Constructing probabilistic graphical model from predicate formulas for fusing logical and probabilistic knowledge

Expressing knowledge as expert experience and discovering knowledge implied in data are two important ways for knowledge acquisition. Consistent combination of these two kinds of knowledge has attracted much attention due to the potential applications to knowledge fusion and wide requirements of decision support. In this paper, we focus on the probabilistic modeling of expert experience represented as logical predicate formulas, aiming at the effective fusion of logical and probabilistic knowledge. Taking qualitative probabilistic network (QPN) as the underlying framework of probabilistic knowledge implied in data as well as the abstraction of general Bayesian networks (BNs), we are to construct the probabilistic graphical model for both the given predicate formulas and the ultimate result of knowledge fusion. We first propose the concept and the construction algorithm of predicate graph (PG) to describe the dependence relations among predicate formulas, and discuss PG’s probabilistic semantics correspondingly. We then prove that PG is a probability dependency model and has the same semantics with a general probabilistic graphical model. Consequently, we give the method for fusing PG and QPN. Experimental results show the effectiveness of our methods.