An Approach to Forgetting in Disjunctive Logic Programs that Preserves Strong Equivalence
This work addresses a specific issue in knowledge representation and reasoning for AI, focusing on incremental improvements in logic programming techniques.
The paper tackles the problem of forgetting atoms in disjunctive logic programs while preserving strong equivalence, resulting in a practical definition that ensures syntax-independence and leads to at worst quadratic blowup in program size.
In this paper we investigate forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. The goal is to provide an approach that is syntax-independent, in that if two programs are strongly equivalent, then the results of forgetting an atom in each program should also be strongly equivalent. Our central definition of forgetting is impractical but satisfies this goal: Forgetting an atom is characterised by the set of SE consequences of the program that do not mention the atom to be forgotten. We then provide an equivalent, practical definition, wherein forgetting an atom $p$ is given by those rules in the program that don't mention $p$, together with rules obtained by a single inference step from rules that do mention $p$. Forgetting is shown to have appropriate properties; as well, the finite characterisation results in a modest (at worst quadratic) blowup. Finally we have also obtained a prototype implementation of this approach to forgetting.