The analysis of the generalized square of opposition
Petra Murinová, Vilém Novák
Available Online August 2013.
- 10.2991/eusflat.2013.42How to use a DOI?
- Fuzzy type theory. Intermediate quantifiers. Generalized Aristotle square of opposition. Complete square of opposition.
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.
- © 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 - 10.2991/eusflat.2013.42 ID - Murinová2013/08 ER -