Integrating Logic into Bayesian Networks Using Natural Deduction Proofs

Natural deduction is a logical system that closely mimics the natural human reasoning process, using not axioms but rather assumptions that are made and later discharged when they are no longer needed. Logical proofs like these, however, lack the ability to handle varying levels of uncertainty and the contradictions that may arise when they are applied to real world situations. The goal of the study described in this paper was to develop a program to convert natural deduction proofs, to be supplied by an automatic theorem prover (ATP), into Bayesian networks, where probabilities can be easily and efficiently adjusted as evidence is found. Because ATPs generally work with resolution proofs, a new specification had to be developed for the input files. The networks were constructed by creating nodes for all formulas and their subformulas, except for context (assumption) nodes and quantifiers, which were handled separately. Ultimately, it is hoped that this conversion project will allow natural deduction to make use of large, existing probabilistic knowledge bases to better process incoming information, but such an objective is beyond the scope of this study.