A fuzzy syllogistic reasoning schema for generalized quantifiers
Fuzzy Sets and SystemsPublished 25 February 2013Open access
Martín Pereira-Fariña, Juan C. Vidal, F. Dĺaz-Hermida, A. Bugarĺn
Citations34
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TL;DR
A new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: a number of different types of quantifiers taken from Theory of Generalized Quantifiers and similarity quantifiers are considered and any number of premises can be taken into account within the reasoning process.
Abstract
In this paper, a new approximate syllogistic reasoning schema is described\nthat expands some of the approaches expounded in the literature into two ways:\n(i) a number of different types of quantifiers (logical, absolute,\nproportional, comparative and exception) taken from Theory of Generalized\nQuantifiers and similarity quantifiers, taken from statistics, are considered\nand (ii) any number of premises can be taken into account within the reasoning\nprocess. Furthermore, a systematic reasoning procedure to solve the syllogism\nis also proposed, interpreting it as an equivalent mathematical optimization\nproblem, where the premises constitute the constraints of the searching space\nfor the quantifier in the conclusion.\n
Keywords
Computer ScienceDecision Sciences
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Studies in cognitive systemsGeneralized Quantifiers and Natural Language
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