An assumption-based truth maintenance system dealing with non-ground justifications

The assumption-based truth maintenance system (ATMS) is a reasoning maintenance system proved useful in many applications and fields such as diagnosis and abductive reasoning. However, one limitation of the ATMS is that it handles propositional justifications only. There are problems, instead, where one has to move to the first-order predicate calculus, and explicitly consider variables. In this paper, we present an extension of the basic ATMS where justifications are definite Horn clauses possibly containing variables, and non-ground terms can occur in ATMS data structures. To maintain the incrementality feature peculiar to the ATMS, we extend the basic label-updating algorithm from the propositional case to the first-order one. In this way, we obtain a system able to produce, for a given atomic formula, the set of minimal hypotheses (possibly containing variables) we have to add to a given theory to prove this formula. We show how this extension relates to logic programs when they are optimized through ...