Non-denoting terms in fuzzy logic: An initial exploration

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901N29" target="_blank" >RIV/61988987:17610/18:A1901N29 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-66830-7_14" target="_blank" >http://dx.doi.org/10.1007/978-3-319-66830-7_14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-66830-7_14" target="_blank" >10.1007/978-3-319-66830-7_14</a>

Result language
angličtina
Original language name
Non-denoting terms in fuzzy logic: An initial exploration
Original language description
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.
Czech name
—
Czech description
—

Project
<a href="/en/project/GA16-19170S" target="_blank" >GA16-19170S: Fuzzy Partial Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Advances in Fuzzy Logic and Technology 2017: Proceedings of: EUSFLAT-2017 - The 10th Conference of the European Society for Fuzzy Logic and Technology
ISBN
978-3-319-66830-7
ISSN
2194-5357
e-ISSN
2194-5365
Number of pages
11
Pages from-to
148-158
Publisher name
Springer International Publishing
Place of publication
Cham
Event location
Warszawa
Event date
Sep 11, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000432315700014

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