Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving (PTP), their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas.
In this proposal, we introduce Bayesian Abductive Logic Programs (BALP), a probabilistic logic that adapts Bayesian Logic Programs (BLPs) for abductive reasoning. Like BLPs, BALPs also combine first-order logic and Bayes nets. However, unlike BLPs, which use deduction to construct Bayes nets, BALPs employ logical abduction. As a result, BALPs are more suited for problems like plan/activity recognition that require abductive reasoning. In order to demonstrate the efficacy of BALPs, we apply it to two abductive reasoning tasks — plan recognition and natural language understanding.
Markov logic networks (MLNs) combine the power of first-order logic and probabilistic graphical models and as a result are ideally suited for solving large, complex problems in application domains that have both rich relational structure and large amount of uncertainty. However, inference in these rich, relational representations is quite challenging. The aim of this thesis is to advance the state-of-the-art in MLN inference, enabling it to solve much harder and more complex tasks than is possible today. To this end, I will develop techniques that exploit logical structures and symmetries that are either explicitly or implicitly encoded in the MLN representation and demonstrate their usefulness by using them to solve hard real-world problems in the field of natural language understanding.
In this paper, we introduce Bayesian Abductive Logic Programs (BALPs), a new formalism that integrates Bayesian Logic Programs (BLPs) and Abductive Logic Programming (ALP) for abductive reasoning. Like BLPs, BALPs also combine first-order logic and Bayesian networks. However, unlike BLPs that use logical deduction to construct Bayes nets, BALPs employ logical abduction. As a result, BALPs are more suited for solving problems like plan/activity recognition and diagnosis that require abductive reasoning. First, we present the necessary enhancements to BLPs in order to support logical abduction. Next, we apply BALPs to the task of plan recognition and demonstrate its efficacy on two data sets. We also compare the performance of BALPs with several existing approaches for abduction.
Kersting, Kristian (Fraunhofer IAIS and University of Bonn) | Russell, Stuart (University of California, Berkeley) | Kaelbling, Leslie Pack (Massachusetts Institute of Technology) | Halevy, Alon (University of Wisconsin Madison) | Natarajan, Sriraam (University of Texas at Austin) | Mihalkova, Lilyana