A Probabilistic Logic for Multi-source Heterogeneous Information Fusion

We investigate methods to define a probabilistic logic and their application to multi-source fusion problems in geospatial decision support systems(1). We begin with a discussion of augmenting propositional calculus with probabilities. Given a set of sentences, S, each with a known probability, the problem is to determine the probability of a query sentence that is a disjunction of literals appearing in S. First, we examine Nilsson's [19] solution based on the semantic models of the sentences; we develop two different approaches to solving the problem as posed: (1) using a linear solver, and (2) geometrically finding the intersection of a line with the probability convex hull. Nilsson's approach provides lower and upper bounds on the solution. We then propose a new approach which finds probabilities for the atoms found in the sentences, and then uses these probabilities to compute the probability of the query sentence. Finally, we describe how this probability representation method can form the basis for a probabilistic logic system to support a multi-source knowledge base for decision support.