An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Fuzzy Sets and Systems
A comprehensive theory of trichotomous evaluative linguistic expressions
Fuzzy Sets and Systems
L-fuzzy quantifiers of type determined by fuzzy measures
Fuzzy Sets and Systems
Triangular norm based predicate fuzzy logics
Fuzzy Sets and Systems
A formal theory of generalized intermediate syllogisms
Fuzzy Sets and Systems
Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices
Information Sciences: an International Journal
Reasoning about mathematical fuzzy logic and its future
Fuzzy Sets and Systems
On the analysis of set-based fuzzy quantified reasoning using classical syllogistics
Fuzzy Sets and Systems
A fuzzy syllogistic reasoning schema for generalized quantifiers
Fuzzy Sets and Systems
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The paper provides a logical theory of a specific class of natural language expressions called intermediate quantifiers (most, a lot of, many, a few, a great deal of, a large part of, a small part of), which can be ranked among generalized quantifiers. The formal frame is the fuzzy type theory (FTT). Our main idea lays in the observation that intermediate quantifiers speak about elements taken from a class that is made ''smaller'' than the original universe in a specific way. Our theory is based on the formal theory of trichotomous evaluative linguistic expressions. Thus, an intermediate quantifier is obtained as a classical quantifier ''for all'' or ''exists'' but taken over a class of elements that is determined using an appropriate evaluative expression. In the paper we will characterize the behavior of intermediate quantifiers and prove many valid syllogisms that generalize classical Aristotle's ones.