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EUSFLAT 2017, IWIFSGN 2017: Advances in Fuzzy Logic and Technology 2017 pp 148-158

# Non-denoting Terms in Fuzzy Logic: An Initial Exploration

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

## Abstract

We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or terms that lack existing referents, e.g., Pegasus, the current king of France, the largest number, or 0/0. Logics designed for this purpose in the classical setting are known as free logics. In this paper we discuss the features of free logics and select the options best suited for fuzzification, deciding on the so-called dual-domain semantics for positive free logic with truth-value gaps and outer quantifiers. We fuzzify the latter semantics in two levels of generality, first with a crisp and subsequently with a fuzzy predicate of existence. To accommodate truth-valueless statements about nonexistent objects, we employ a recently proposed first-order partial fuzzy logic with a single undefined truth value. Combining the dual-domain semantics with partial fuzzy logic, we define several kinds of ‘inner-domain’ quantifiers, relativized by the predicate of existence. Finally, we make a few observations on some of the resulting rules of free fuzzy quantification that illustrate the differences between the two proposed systems of free fuzzy logic and their well known non-free or non-fuzzy variants.

## Keywords

Quantifier Free logic Existence Referent Partial fuzzy logic

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## Copyright information

© Springer International Publishing AG 2018

## Authors and Affiliations

1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of Ostrava, NSC IT4InnovationsOstravaCzech Republic