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194.4. Il Cervino di Varzi: similarità e oggetti vaghiRivista di Estetica 49 281-296. 2012.In the framework of fuzzy logic a definition of vague object is proposed based on the notion of fuzzy equivalence. Indeed, while a crisp object is defined as a “concrete thing” together with an equivalence, I propose to define a vague object as a “concrete thing” together with a fuzzy equivalence.
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18Approximate Reasoning Based on SimilarityMathematical Logic Quarterly 46 (1): 77-86. 2000.The connection between similarity logic and the theory of closure operators is examined. Indeed one proves that the consequence relation defined in [14] can be obtained by composing two closure operators and that the resulting operator is still a closure operator. Also, we extend any similarity into a similarity which is compatible with the logical equivalence, and we prove that this gives the same consequence relation
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16Decidability, Recursive Enumerability and Kleene Hierarchy For L‐SubsetsMathematical Logic Quarterly 35 (1): 49-62. 1989.
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14Approximate Similarities and Poincaré ParadoxNotre Dame Journal of Formal Logic 49 (2): 203-226. 2008.De Cock and Kerre, in considering Poincaré paradox, observed 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 with which to face the question. 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 space…Read more
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14Measures in Euclidean Point-Free Geometry (an exploratory paper)Logic and Logical Philosophy 1-20. forthcoming.We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.
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12Pavelka's Fuzzy Logic and Free L‐SubsemigroupsMathematical Logic Quarterly 31 (7‐8): 123-129. 1985.
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6TuringL-machines and recursive computability forL-mapsStudia Logica 48 (2): 179-192. 1989.We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.
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La relazione di connessione in AN Whitehead: Aspetti matematiciEpistemologia 15 (2): 351-364. 1992.