A function-free rule language based on definite first-order Horn clauses, normally with safety conditions on rule variables. Positive Datalog has a least Herbrand model obtained by forward chaining.
Datalog allowing disjunctions of positive atoms in rule heads. A satisfiable program can have incomparable minimal Herbrand models and no least Herbrand model.
Datalog with negative body premises. Its meaning depends on the specified semantics, such as stable model semantics or evaluation of a stratified Datalog program.
A Datalog with negation program whose predicates can be assigned levels so that positive premises do not exceed their head's level and negative premises have strictly lower levels. Finite programs of this form can be evaluated stratum by stratum and have a unique stable model.
A semantics in which an interpretation must equal the least Herbrand model of its own stable model reduct. Some programs have no stable model, and others have several.
A consequence holds skeptically if it is true in every admitted model, in particular every stable model when using stable model semantics. Exhibiting one supporting stable model establishes only existence of support, not skeptical entailment.
Ground the rules, delete every rule having a negative body atom true in the candidate , and remove all remaining negative premises. The result is a positive program whose least Herbrand model is compared with .
A Herbrand interpretation equal to the least Herbrand model of the positive reduct obtained relative to that interpretation.
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