Why Some Non-classical Logics Are More Studied?
- 4 Downloads
It is well known that the traditional 2-valued logic is only an approximation to how we actually reason. To provide a more adequate description of how we actually reason, researchers proposed and studied many generalizations and modifications of the traditional logic, generalizations and modifications in which some rules of the traditional logic are no longer valid. Interestingly, for some of such rules (e.g., for law of excluded middle), we have a century of research in logics that violate this rule, while for others (e.g., commutativity of “and”), practically no research has been done. In this paper, we show that fuzzy ideas can help explain why some non-classical logics are more studied and some less studied: namely, it turns out that most studied are the violations which can be implemented by the simplest expressions (specifically, by polynomials of the lowest order).
This work was supported in part by the National Science Foundation via grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).
- 2.Bouchon-Meunier, B., Kreinovich, V., Nguyen, H.T.: Non-associative operations. In: Proceedings of the Second International Conference on Intelligent Technologies InTech 2001, Bangkok, Thailand, 27–29 November 2001, pp. 39–46 (2001)Google Scholar
- 5.Kreinovich, V.: Towards more realistic (e.g., non-associative) ‘and’- and ‘or’-operations in fuzzy logic. Soft Comput. 8(4), 274–280 (2004)Google Scholar
- 6.Martinez, J., Macias, L., Esper, A., Chaparro, J., Alvarado, V., Starks, S.A., Kreinovich, V.: Towards more realistic (e.g., non-associative) and- and or-operations in fuzzy logic. In: Proceedings of the 2001 IEEE Systems, Man, and Cybernetics Conference, Tucson, Arizona, 7–10 October 2001, pp. 2187–2192 (2001)Google Scholar
- 13.Xiang, G., Kreinovich, V.: Towards improved trapezoidal approximation to intersection (fusion) of trapezoidal fuzzy numbers: specific procedure and general non-associativity theorem. In: Proceedings of the IEEE World Congress on Computational Intelligence WCCI 2010, Barcelona, Spain, 18–23 July 2010, pp. 3120–3125 (2010)Google Scholar