Poincaré Paradox and Approximate Similarities
نویسنده
چکیده
This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity” cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools to face the question with. Indeed a first order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established. Keyword: Fuzzy equivalence, approximate reasoning, point-free geometry, Poincaré paradox.
منابع مشابه
Poincaré Paradox, Similarities and Point-free Geometry. (brief Version of a Paper Named " Similarities, Approximate Objects and Paradoxes " Submitted to Fuzzy Sets and Systems)
1. Introduction Recall that a fuzzy equivalence relation in a nonempty set S is a fuzzy relation eq : S×S → [0,1] such that eq(x,x) = 1 (reflexive); eq(x,y) = eq(y,x) (symmetric) ; eq(x,y)≈eq(y,z) ≤ eq(x,z) (≈-transitive) where ≈ is a t-norm. Now, as observed by De Cock and Kerre in [3], this notion is not suitable to model approximate equality and therefore to solve paradoxes like the so calle...
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