TY - JOUR
ID - 1981
TI - EQ-logics with delta connective
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Dyba, M.
AU - Novak, V.
AD - University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
Y1 - 2015
PY - 2015
VL - 12
IS - 2
SP - 41
EP - 61
KW - EQ-algebra
KW - EQ-logic
KW - Equational logic
KW - Delta connective
KW - Generalized deduction theorem
DO - 10.22111/ijfs.2015.1981
N2 - 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.
UR - https://ijfs.usb.ac.ir/article_1981.html
L1 - https://ijfs.usb.ac.ir/article_1981_f9c205b6a230d24728542018f1b3f176.pdf
ER -