Reasoning with recursive loops under the PLP framework

Abstract

Recursive loops in a logic program present a challenging problem to the PLP (Probabilistic Logic Programming) framework. On the one hand, they loop forever so that the PLP backward-chaining inferences would never stop. On the other hand, they may generate cyclic influences, which are disallowed in Bayesian networks. Therefore, in existing PLP approaches, logic programs with recursive loops are considered to be problematic and thus are excluded. In this article, we propose a novel solution to this problem by making use of recursive loops to build a stationary dynamic Bayesian network. We introduce a new PLP formalism, called a Bayesian knowledge base . It allows recursive loops and contains logic clauses of the form A ← A 1 ,…, A l , true , Context , Types , which naturally formulate the knowledge that the A i s have direct influences on A in the context Context under the type constraints Types . We use the well-founded model of a logic program to define the direct influence relation and apply SLG-resolution to compute the space of random variables together with their parental connections. This establishes a clear declarative semantics for a Bayesian knowledge base. We view a logic program with recursive loops as a special temporal model, where backward-chaining cycles of the form A ← … A ← … are interpreted as feedbacks. This extends existing PLP approaches, which mainly aim at (nontemporal) relational models.