@article {
author = {Dyba, M. and Novak, V.},
title = {EQ-logics with delta connective},
journal = {Iranian Journal of Fuzzy Systems},
volume = {12},
number = {2},
pages = {41-61},
year = {2015},
publisher = {University of Sistan and Baluchestan},
issn = {1735-0654},
eissn = {2676-4334},
doi = {10.22111/ijfs.2015.1981},
abstract = {In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binaryoperations of fuzzy equality and multiplication. EQ-algebra generalizesresiduated lattices, namely, every residuated lattice is an EQ-algebra but notvice-versa.In this paper, we introduce additional connective $logdelta$ in EQ-logics(analogous to Baaz delta connective in MTL-algebra based fuzzy logics) anddemonstrate that the resulting logic has again reasonable properties includingcompleteness. Introducing $Delta$ in EQ-logic makes it possible to prove alsogeneralized deduction theorem which otherwise does not hold in EQ-logics weakerthan MTL-logic.},
keywords = {EQ-algebra,EQ-logic,Equational logic,Delta connective,Generalized deduction theorem},
url = {https://ijfs.usb.ac.ir/article_1981.html},
eprint = {https://ijfs.usb.ac.ir/article_1981_f9c205b6a230d24728542018f1b3f176.pdf}
}