Revision by expansion in logic programs

Abstract

We discuss the general problem of revising a contradictory non-monotonic theory and we show that sometimes expanding the theory is more appropriate than contracting it in order to remove the contradiction. We apply this idea of theory-expansion to logic programs with negation and constraints.

Using the well-founded (wf-) model semantics for logic programs as our starting point we show that this model may be contradictory due to a clash between the assumption made in the wf-model to consider unfounded atoms to be false and the repercussions constraints can have on this assumption.

Then we show that the contradiction can be removed by adding rules to unfounded atoms in the program. We propose to use the noncontradictory wf-model of such an expansion as the semantics of the original program.

We develop a formal framework for program expansion, studying properties as completeness, minimality and computational complexity of expansions.

We think that program expansion is the best framework to study procedurally defined revision processes as proposed in truth maintenance and logic programming such as dependency-directed backtracking and the recently proposed contradiction removal semantics.

Using the framework of program expansions we are able to determine the complexity profiles of these approaches as well as significant generalizations of both of them.