The analysis of the generalized square of opposition

DOI

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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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  - 10.2991/eusflat.2013.42
ID  - Murinová2013/08
ER  -