Model states revisited

Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the...

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Bibliographische Detailangaben
1. Verfasser:	Volger, Hugo (VerfasserIn)
Format:	UnknownFormat
Sprache:	eng
Veröffentlicht:	Passau 1995
Schriftenreihe:	Universität <Passau> / Fakultät für Mathematik und Informatik: MIP 1995,22
Schlagworte:	Disjunction (Logic) > Herbrand's theorem (Number theory) > Logic programming > Theoretische Informatik > Mathematik > Informatik
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Zusammenfassung:	Abstract: "Logic programs posess a unique smallest Herbrand model, the initial model semantics. In addition, the smallest Herbrand model of a logic program can be constructed as least fixpoint of an appropriate closure operator on Herbrand structures. This is the initial model semantics of the logic program. Replacing logic programs by the more general disjunctive logic programs where we admit disjunctions in the head of rules we have the following situation. However, a disjunctive fact has several different minimal Herbrand models. Hence, disjunctive logic programs posess in general a set of minimal Herbrand models, the minimal model semantics. To obtain an analogous fixpoint characterization one has to collect the Herbrand structures into one object. Therefore Lobo, Minker, Rajasekar (cf.[5]) have introduced the notion of a model state of a disjunctive logic program where disjunctions of ground goals replace the ground goals. -- However, a small counterexample shows that their definition needs to be corrected. In this paper we introduce an improved definition and develop carefully the correspondence between states and their saet [sic] of structures. As a pay-off we obtain a generalization of the results to states for 3-valued Herbrand structures. Since 3-valued Herbrand structures are described by negated and unnegated ground goals, the generalized Herbrand states consist of disjunctions of negated and unnegated ground goals. The 3-valued minimal model semantics yields a minimal-maximal model semantics of Herbrand structures."
Beschreibung:	7, 3 S.