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EQ-logics with delta connective | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 12، شماره 2، تیر 2015، صفحه 41-61 اصل مقاله (334.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2015.1981 | ||
| نویسندگان | ||
| M. Dyba* ؛ V. Novak | ||
| University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava, Czech Republic | ||
| چکیده | ||
| In this paper we continue development of formal theory of a special class of fuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of the MTL-logic in which the basic connective is implication, the basic connective in EQ-logics is equivalence. Therefore, a new algebra of truth values called EQ-algebra was developed. This is a lower semilattice with top element endowed with two binary operations of fuzzy equality and multiplication. EQ-algebra generalizes residuated lattices, namely, every residuated lattice is an EQ-algebra but not vice-versa. In this paper, we introduce additional connective $logdelta$ in EQ-logics (analogous to Baaz delta connective in MTL-algebra based fuzzy logics) and demonstrate that the resulting logic has again reasonable properties including completeness. Introducing $Delta$ in EQ-logic makes it possible to prove also generalized deduction theorem which otherwise does not hold in EQ-logics weaker than MTL-logic. | ||
| کلیدواژهها | ||
| EQ-algebra؛ EQ-logic؛ Equational logic؛ Delta connective؛ Generalized deduction theorem | ||
| مراجع | ||
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