Rule-PSAT: Relaxing Rule Constraints in Probabilistic Assumption-Based Argumentation

Probabilistic rules are at the core of probabilistic structured argumentation. With a language L, probabilistic rules describe conditional probabilities Pr(sigma(0) | sigma(1),..., sigma(k)) of deducing some sentences sigma(0) is an element of L from others sigma(1),..., sigma(k) is an element of L by means of prescribing rules sigma(0) <- sigma(1),..., sigma(k) with head sigma(0) and body sigma(1),..., sigma(k). In Probabilistic Assumption-based Argumentation (PABA), a few constraints are imposed on the form of probabilistic rules. Namely, (1) probabilistic rules in a PABA framework must be acyclic, and (2) if two rules have the same head, then the body of one rule must be the subset of the other. In this work, we show that both constraints can be relaxed by introducing the concept of Rule Probabilistic Satisfiability (Rule-PSAT) and solving the underlying joint probability distribution on all sentences in L. A linear programming approach is presented for solving Rule-PSAT and computing sentence probabilities from joint probability distributions.