Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
A formal theory of intermediate quantifiers
Fuzzy Sets and Systems
Monadic L-fuzzy quantifiers of the type
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
A fuzzy syllogistic reasoning schema for generalized quantifiers
Fuzzy Sets and Systems
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In this paper, we continue developing the formal theory of intermediate quantifiers (expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of). The theory is a fuzzy-logic formalization of the concept introduced by Peterson in his book. We will syntactically prove that 105 generalized Aristotle's syllogisms introduced in this book are valid in our theory. At the same time, we will also prove that syllogisms listed there as invalid are invalid also in our theory. Therefore, we believe that our theory provides a reasonable mathematical model of the generalized syllogistics.