Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/9362
Title: Symmetric properties of the syllogistic system inherited from the square of opposition
Authors: Kumova, Bora İsmail
Keywords: Fuzzy logic
Reasoning
Set theory
Syllogisms
Publisher: Birkhäuser
Series/Report no.: Studies in Universal Logic
Abstract: The logical square Omega has a simple symmetric structure that visualises the bivalent relationships of the classical quantifiers A, I, E, O. In philosophy it is perceived as a self-complete possibilistic logic. In linguistics however its modelling capability is insufficient, since intermediate quantifiers like few, half, most, etc cannot be distinguished, which makes the existential quantifier I too generic and the universal quantifier A too specific. Furthermore, the latter is a special case of the former, i.e. A subset of I, making the square a logic with inclusive quantifiers. The inclusive quantifiers I and O can produce redundancies in linguistic systems and are too generic to differentiate any intermediate quantifiers. The redundancy can be resolved by excluding A from I, i.e. I-2=I-A, analogously E from O, i.e. O-2=O-E. Although the philosophical possibility of A subset of I is thus lost in I-2, the symmetric structure of the exclusive square (2)Omega remains preserved. The impact of the exclusion on the traditional syllogistic system S with inclusive existential quantifiers is that most of its symmetric structures are obviously lost in the syllogistic system S-2 with exclusive existential quantifiers too. Symmetry properties of S are found in the distribution of the syllogistic cases that are matched by the moods and their intersections. A syllogistic case is a distinct combination of the seven possible spaces of the Venn diagram for three sets, of which there exist 96 possible cases. Every quantifier can be represented with a fixed set of syllogistic cases and so the moods too. Therefore, the 96 cases open a universe of validity for all moods of the syllogistic system S, as well as all fuzzy-syllogistic systems S-n, with n-1 intermediate quantifiers. As a by-product of the fuzzy syllogistic system and its properties, we suggest in return that the logical square of opposition can be generalised to a fuzzy-logical graph of opposition, for 2<n.
URI: https://doi.org/10.1007/978-3-319-45062-9_6
https://hdl.handle.net/11147/9362
ISBN: 978-3-319-45062-9
Appears in Collections:Computer Engineering / Bilgisayar Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Files in This Item:
File SizeFormat 
kumova2017.pdf1.13 MBAdobe PDFView/Open
Show full item record



CORE Recommender

SCOPUSTM   
Citations

1
checked on Apr 5, 2024

Page view(s)

98
checked on Apr 8, 2024

Download(s)

64
checked on Apr 8, 2024

Google ScholarTM

Check




Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.