University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065412220150429EQ-logics with delta connective4161198110.22111/ijfs.2015.1981ENM.DybaUniversity of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech RepublicV.NovakUniversity of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech RepublicJournal Article20130225In this paper we continue development of formal theory of a special class of<br />fuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of the<br />MTL-logic in which the basic connective is implication, the basic connective in<br />EQ-logics is equivalence. Therefore, a new algebra of truth values called<br />EQ-algebra was developed. This is a lower semilattice with top element endowed with two binary<br />operations of fuzzy equality and multiplication. EQ-algebra generalizes<br />residuated lattices, namely, every residuated lattice is an EQ-algebra but not<br />vice-versa.<br />In this paper, we introduce additional connective $logdelta$ in EQ-logics<br />(analogous to Baaz delta connective in MTL-algebra based fuzzy logics) and<br />demonstrate that the resulting logic has again reasonable properties including<br />completeness. Introducing $Delta$ in EQ-logic makes it possible to prove also<br />generalized deduction theorem which otherwise does not hold in EQ-logics weaker<br />than MTL-logic.https://ijfs.usb.ac.ir/article_1981_f9c205b6a230d24728542018f1b3f176.pdf