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General patterns for nonmonotonic reasoning: From basic entailments to plausible relations. (English) Zbl 0966.03024

The paper is aiming at a general characterization of nonmonotonic reasoning in the style of Gabbay, Makinson, Kraus, Lehman, Magidor and others. A sequence of generalizations of the previous work in the field is presented in the paper. An ambition of the authors is to reach a better understanding of the conditions that a plausible relation for nonmonotonic reasoning should satisfy.
First, the condition of supraclassicality is generalized – instead of using classical entailment relation as the basis for definitions of nonmonotonic entailment relations, the use of any entailment relation which satisfies certain minimal conditions is allowed.
Second, Tarskian consequence relations are used instead of entailment relations – a set of premises is considered rather than a single one.
Third, the approach is aiming at language-independence – almost all the conditions on the underlying language are removed.
Finally, consequence relations with multiple conclusions are allowed.
The developed framework is able to reflect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning.
The paper is divided into two main sections. The first of them studies nonmonotonic reasoning on the syntactical level. The sequence of generalizations (resulting in corresponding frameworks) is presented. The sequence of frameworks culminates in a notion of plausible nonmonotonic consequence relation (with an ambition to capture the intuitive idea of “correct” nonmonotonic reasoning). The next section provides a general semantic method for constructing plausible nonmonotonic consequence relations. The method combines a lattice-valued semantics with a preferential semantics.

MSC:

03B60 Other nonclassical logic
68T27 Logic in artificial intelligence
03B53 Paraconsistent logics
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