Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)

The analysis of the generalized square of opposition

Authors
Petra Murinová, Vilém Novák
Corresponding Author
Petra Murinová
Available Online August 2013.
DOI
https://doi.org/10.2991/eusflat.2013.42How to use a DOI?
Keywords
Fuzzy type theory. Intermediate quantifiers. Generalized Aristotle square of opposition. Complete square of opposition.
Abstract

In this paper, we continue development of a formal theory of intermediate quantifiers (linguistic expressions such as ``most'', ``many'', ``few'', ``almost all'', etc.). In previous work, we demonstrated that 105 generalized syllogisms are valid in our theory. We turn our attention to another problem which is analysis of the generalized Aristotelian square of opposition which, besides the classical quantifiers, is extended also by several selected intermediate quantifiers. We show that the expected relations can be well modeled in our theory. The formal theory of intermediate quantifiers is developed within a special higher-order fuzzy logic --- L ukasiewicz fuzzy type theory.

Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
Series
Advances in Intelligent Systems Research
Publication Date
August 2013
ISBN
978-90786-77-78-9
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2013.42How to use a DOI?
Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Petra Murinová
AU  - Vilém Novák
PY  - 2013/08
DA  - 2013/08
TI  - The analysis of the generalized square of opposition
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 292
EP  - 299
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.42
DO  - https://doi.org/10.2991/eusflat.2013.42
ID  - Murinová2013/08
ER  -