Document Zbl 1280.68245

Beierle, Christoph; Kern-Isberner, Gabriele

Semantical investigations into nonmonotonic and probabilistic logics. (English) Zbl 1280.68245

Ann. Math. Artif. Intell. 65, No. 2-3, 123-158 (2012).

Summary: Different forms of semantics have been proposed for conditionals of the form “Usually, if A then B”, ranging from quantitative probability distributions to qualitative approaches using plausibility orderings, possibility distributions, or conditional objects. Atomic-bound systems, also called big-stepped probabilities, allow qualitative reasoning with probabilities, aiming at bridging the gap between qualitative and quantitative argumentation and providing a model for the nonmonotonic reasoning system P. By using Goguen and Burstall’s notion of institutions for the formalization of logical systems, we elaborate precisely which formal connections exist among big-stepped probabilities, standard probabilities, and qualitative logics. Based on our investigations, we also develop two variants of conditional objects, one of them having a simpler semantics while still providing a model for system P.

Cited in 9 Documents

MSC:

68T27	Logic in artificial intelligence
68T30	Knowledge representation
68T37	Reasoning under uncertainty in the context of artificial intelligence

Keywords:

conditional logic; probabilistic logic; qualitative logic; big-stepped probability; conditional object; institution; institution morphism

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References:

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