デフォルト推論における非再帰的拡張世界とその性質

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Nonrecursive extension in default reasoning is introduced and its properties are discussed. It is well known that traditional logical reasoning is always monotonic, i. e., the set of theorems increases monotonically with the set of axioms. R. Reiter proposed a default logic as a means for drawing conclusions based on incomplete axioms. Since such plausible conclusions can be invalidated when this partial world description is supplemented by new information, the logic is called nonmonotonic logic. Nonmonotonic reasoning based on the logic is suitable for commonsense reasoning or incomplete knowledge reasoning in knowledge engineering system. In Reiter's default reasoning system the set of all beliefs (1st order theorems) derivable from a default theory is called "extension". The extension is one of the most significant concept in default reasoning, and it is essential in analysis of a default theory. A formal definition of the extension given by Reiter is written recursively (i. e., the extension is defined using the extension in itself). Then it can not explain our deduction process because it has a contradiction in causality (i. e., it requires the consequents of the deduction during its deduction process). Since the nonrecursive extension proposed in this paper is defined by a nonrecursive deduction procedure, it has similar property with our deduction process and it can be obtained easily. It is proved that when only one extension exists, the nonrecursive extension is identical with it, and when many extensions exist, the nonrecursive extension is identical with one of the extensions under the condition that the nonrecursive extension is satisfiable.
社団法人人工知能学会の論文
1988-05-20

デフォルト推論における非再帰的拡張世界とその性質

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