On inferring the most probable sentences in Bayesian logic

Vast literature and accumulating data in biomedicine creates a challenging problem. On the one hand, the literature and the curated ontologies, as a huge logical knowledge base, offer tremendous amount of raw factual knowledge. On the other hand, the biological data and its Bayesian probabilistic modeling bring in inherent uncertainty about models, model properties, or predictions. The fusion of such textually oriented logical knowledge and complex probabilistic models prompted active research, including research on probabilistic first-order logic or on more powerful probabilistic models. In the paper, we introduce a method for fusing logical knowledge bases and complex, multivariate distributions inducing probability for firstorder sentences. We present an extended firstorder logic language with predicates and functions oriented towards graphical models. Furthermore, within this framework, we formulate the concept of “most probable sentences”, which is a first-order generalization of the “most probable explanation” problem. We characterize the approaches, present the statistical analysis of the problem, and describe integrated “search-andestimate” methods. Finally we report preliminary results for a real world medical problem.