Traditionally, approaches to abductive reasoning have either been based on first-order logic, by determining assumptions sufficient to deduce the observations to be explained, or based on Bayesian networks, by using probabilistic inference to compute the posterior probability of alternative explanations given a set of observations. Both of these approaches have significant limitations. The logical approach is unable to reason under uncertainty and estimate the likelihood of alternative explanations. The Bayes-net approach is unable to handle structured representations, and therefore is incapable of effectively reasoning about situations involving multiple entities with various relations between them.

Weighted abduction, developed by Hobbs and others, is arguably the most sophisticated approach to abduction to date. It is logic-based, but has some of the desirable features of probabilistic methods. It is able to exploit implicit redundancy, plausibility, and relevance to the topic at hand, and it has been applied successfully in natural language processing. But the weighting scheme does not have a solid theoretical basis, and it is not clear how to deal with noisy and incomplete observations.

In this project, we will develop a unified approach to abductive inference, combining the capabilities of logic and probability, formalizing weighted abduction, and extending it to handle a variety of important phenomena. We will use Markov logic as the formal language. Markov logic unifies first-order logic and probability into a single coherent representation. We will build on the full complement of efficient inference and learning algorithms for Markov logic available in the open-source Alchemy package. Our research will fall into five main strands: foundations, real-world issues, scaling up, cognitive modeling, and applications. We will apply the results to plan recognition and behavior interpretation, with evidence ranging from sensor networks to text and images.