Recursive loops in a logic program present a challenging problem to the PLP framework. On the one hand, they loop forever so that the PLP backward-chaining inferences would never stop. On the other hand, they 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 paper, we propose an approach that makes use of recursive loops to build a stationary dynamic Bayesian network. Our work stems from an observation that recursive loops in a logic program imply a time sequence and thus can be used to model a stationary dynamic Bayesian network without using explicit time parameters. We introduce a Bayesian knowledge base with logic clauses of the form @math , which naturally represents the knowledge that the @math s have direct influences on @math in the context @math under the type constraints @math . We then 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. We introduce a novel notion of influence clauses, based on which a declarative semantics for a Bayesian knowledge base is established and algorithms for building a two-slice dynamic Bayesian network from a logic program are developed.
Third, most importantly PKB has no mechanism for handling cyclic influences. In PKB, cyclic influences are defined to be inconsistent (see Definition 9 of the paper @cite_10 ) and thus are excluded (PKB excludes cyclic influences by requiring its programs be acyclic). In BKB, however, cyclic influences are interpreted as feedbacks, thus implying a time sequence. This allows us to derive a stationary DBN from a logic program with recursive loops.
@cite_10
2000805332
We define a language for representing context-sensitive probabilistic knowledge. A knowledge base consists of a set of universally quantified probability sentences that include context constraints, which allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language. We present a query answering procedure that takes a query Q and a set of evidence E and constructs a Bayesian network to compute P(Q¦E). The posterior probability is then computed using any of a number of Bayesian network inference algorithms. We use the declarative semantics to prove the query procedure sound and complete. We use concepts from logic programming to justify our approach.