Unfounded sets and well-founded semantics for general logic programs

Abstract

A general logic program (abbreviated to "prog-ram hereafter) I a eet of ruler that have both positive and negative subgoals It 1s common to view a deductive database as a general logic program conslating of rulea (IDB) slttmg above elementary relatlone (EDB, facts)It 18 deelrable to aseoclate one Herbrand model with a program and think of that model ae the =meanmg of the program," or Its "declarative semantlce." Ideally, queries dlrected to the program would be anewered in accordance with this model We mtroduce unbunded sets and well-founded pa&al modeb, and define the well-founded eemantlcs of a program to be Its wellfounded partial model If the well-founded partial model 18 m fact a model, we call it the well-founded model, and eay the program IU 'well-behaved n We show that the class of well-behaved programs properly Includes previously studied classes of %tratifiedD and "locally stratified' programs Gelfond and kfschits have propoeed a definltlon of 'unique stable model" for general logic programs We show that a program hae a umque stable model d It has a well-founded model, in which case they are the same We discuss why the convene M not true

Extended RDF: Computability and complexity issues

“…Hybrid rules should be safe, that is, each variable in the head of the rule, each variable in one of the weakly-negated datalog atoms in the body of the rule, and each free variable in the DL constraint in the body of the rule should be bound in the DL constraint to a constant or to a variable appearing in one of the positive datalog atoms in the body of the rule. The proposed semantics for a hybrid program is defined as a generalization of the well-founded semantics of normal programs [27]. However, in this work, rule-based reasoning is supported only for datalog atoms.…”

Shinren: Non-monotonic Trust Management for Distributed Systems

“…However, REFEREE and TES do not have formally defined semantics. RT is based on the well-founded semantics which is a non-monotonic semantics proposed originally for logic programming with negation [11]. The problem with using well-founded semantics in trust management is that it is based on the closed world assumption (CWA) and the uniformity of CWA may lead to counter-intuitive results.…”

Computing Fuzzy Answer Sets Using dlvhex

“…To trace such intuitively incorrect fuzzy models, [17] defines a fuzzy version of the classical unfounded set characterisation [16,14] of ASP. To obtain this fuzzy variant, one needs to define for each rule r in the program a subset Y of L such that assigning any value from Y to the head of r does not lower r's degree of satisfaction.…”

“…An alternative characterization of answer sets is given in [16,14] in terms of unfounded sets. Intuitively, an unfounded set is a set of literals for which there is no motivation to suppose that these literals have to be true.…”