Logic-based order of magnitude qualitative reasoning for closeness via proximity intervals: a first approach
نویسندگان
چکیده
Qualitative reasoning is an area of AI which provides solutions to problems where the quantitative information either is not available or can not be used; in particular, order of magnitude qualitative reasoning assumes different qualitative classes and relations such as negligibility and closeness. In this paper, we focus mainly on the very important notion of closeness from the logical point of view, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We introduce a multimodal logic for order of magnitude reasoning which includes the notions of closeness and negligibility, we provide an axiom system, which is sound and complete.
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