Constraints, Causal Rules and Minimal Change in Model-based Update

We consider knowledge base update while the domain constraints are explicitly taken into account. We argue that the traditional constraint form is problematic to capture the causality of the domain, and ignoring this point may lead to difficulties in knowledge base updates. To handle this problem properly, it is necessary to describe the causal rules of the domain explicitly in the update formalism. Unlike other researchers viewing causal rules as some kind of inference rules, we distinguish causal rules between defeasible and non-defeasible cases. It turns out that a causality-based update theory in our formalism can be specified as a Reiter's closed default theory while defeasible causal rules correspond to closed normal defaults and non-defeasible causal rules correspond to closed defaults without justification. By using Lukaszewicz's model default theory, we provide a formal semantics for our causal rules. We then propose a causality-based minimal change approach for representing update, and show that our approach provides plausible solutions for model-based updates. We also investigate the properties of our approach and show that our approach generalizes the classical PMA update theory [4] and a recent causality-based update method [2].