The BG Family: Facts, Rules and Constraints

In this chapter, we present a family of reasoning models which generalizes the models seen so far. The DEDUCTION problem, expressed in a generic way, takes a knowledge base K and a goal Q as input, and asks whether Q can be deduced from K. Depending on the knowledge base composition, different models are obtained. If K is composed of facts only, we obtain the BG (or SG) model studied in the first chapters. When rules are added, we obtain the model studied in the preceding chapter. Now we will also consider graph positive and negative constraints, which introduce another problem, i.e., CONSISTENCY (“Is the knowledge base consistent with respect to the constraints?”) Deduction from inconsistent bases is forbidden. Depending on how rules and constraints are combined, rules have different semantics and become inference rules or evolution rules. Inference rules represent implicit knowledge and evolution rules represent possible actions transforming factual knowledge (which is possibly enriched by applications of inference rules).