On Conjectures in t-Norm Based Fuzzy Logics
This paper is a humble homage to Enric Trillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of these models, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics. We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence operators definable in these logics, namely the ones corresponding to the so-called truth-preserving and degree-preserving consequence relations. We pay special attention to the particular cases of three prominent fuzzy logics: Gödel, Product and Łukasiewicz logics
KeywordsCHC models Consequence operators t-norm based fuzzy logics Consistency Conjectures
This work has been partially supported by the Spanish projects TIN2012-39348-C02-01 (Esteva and Godo) and TIN2011-29827-C02-01 (García-Honrado).
- 7.Cintula, P., Hájek, P., Noguera, C.: Handbook of Mathematical Fuzzy Logic (in 2 volumes). of Studies in Logic, Mathematical Logic and Foundations, vols. 37–38 College Publications, London (2011)Google Scholar
- 12.Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput. 4(2), 106–112 (2000)Google Scholar
- 13.Ertola, R., Esteva, F., Flaminio, T., Godo, L., Noguera, C.: Paraconsistency properties in degree-preserving fuzzy logics. Soft Comput. J. 19(3), 531–546 (2015)Google Scholar