3値アブダクション枠組における一貫性制約と意味論
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概要
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Abduction is a form of nonmonotonic reasoning. It is constituted by an abduction framework (P^*, Ab^*, 1^*), where P^* is an abductive program, Ab^* is a set of abducible atoms and I^* is an integrity constraint. Its declarative semantics is defined by abductive extensions P^* ∪Δ such that Δ ⊆ Ab^* and P^* ∪ Δ satisfies I^*. Eshghi and Kowalski (1989) have given the abduction framework whose declarative semdntics is equal to (2-valued) stable models and the abductive proof procedure to obtain an abductive explanation for a query. But this procedure is not sound with respect to this semantics. Dung (1991) has shown proper semantics, e.g. preferred extension, which generalizes other declarative semantics for normal logic programs. The abductive proof procedure is sound with respect to Dung's semantics. In this paper, we establish an abduction framework which is based on 3-valued logic. It is realized by dealing with the abductive adjustment which is a set of abducible atoms interpreted undefined. In 3-valued abduction framework, its declarative semantics is defined by 3-valued abductive extensions P^* ∪ Γ^u ∪ Δ. While Dung's semantics is in terms of the notion of acceptability in addition to the integrity constraint, our semantics only relies on the integrity constraint. This paper shows that their semantics are equivalent. We also present the relations between our framework and the alternating fixpoint by van Gelder (1993). Finally, we have the relations amont Dung's abduction framework, our 3-valued abduction framework and alternating fixpoint.
- 社団法人人工知能学会の論文
- 1999-05-01
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