Logic Programs with Refutation Rules

We extend logic programming to deal with theories that include both ordinary clauses and new refutation rules. While the ordinary rules are supposed to add knowledge, when they are activated, the refutation rules are supposed to remove knowledge. Such kind of rules are important in the areas where reasoning with mixed rules is advocated: decision support systems, normative domains governed by implicit or explicit regulations, case based reasoning and problem solving methods for assessment tasks.

For example default logic can be considered as a system that operates with rules of the form: if δj are accepted and σj are not accepted (-σj are consistent with the current state) then I is accepted. Loosely this is also the meaning of a clause l ← σj, ← ||σj according to stable model semantics. In fact any maximal consistent set of such rules from a given default system or a normal logic program define an extension in default logic or stable model in Stable Model Semantics correspondingly. We propose to extend logic programming to reason with refutation rules that explicitly states which sentences to be removed if some others are accepted. Loosely refutation rules have the form: if Oi are accepted and σj are not accepted then I should be rejected. We also insist that after removing of certain sentences, the reasons for these changes should remain unchanged.

To adapt logic programming to manage with such kind of mixed reasoning two alternative decisions are proposed to modify Two Valued and Three Valued Stable Model Semantics by giving a higher priority to refutation rules.

We also propose a transformation which eliminates refutation rules by using negation by failure over the initial language augmented with a new test operator. To proof that the proposed transformation preserves the original meaning of the program and the refutation rules we prolong Stable Model Semantics and Three Valued Stable Model Semantics to programs that include test sentences.

We extend our results to include disjunctive logic programs. The transformed programs can be implemented by logic programming methods that implement stable models semantics.