n-Fold implicative basic logic is Gödel logic

Abstract

We prove that Haveshki's and Eslami's n-fold implicative basic logic is Gödel logic and n-fold positive implicative basic logic is a fragment of ukasiewicz logic.

Modal representation of coalgebras over local BL-algebras

“…Deductive systems have been widely studied in BL-algebras namely to characterize fragments of Basic fuzzy logic (see [15]); it is obvious that for a non-empty subset F of L, F is a deductive system if and only if it is a filter.…”

“…The following are equivalent: (iv) [ [15], Example 1] The chain {0, x, y, 1}, with the operations * and → defined by the following tables * 0 x y 1 0 0 0 0 0 x 0 0 x x y 0 x y y 1 0 x y 1…”

Fuzzyn-Fold Filters of Pseudoresiduated Lattices

“…In the folding approach, Haveshki and Eslami introduced the notion of -fold implicative (resp., -fold positive implicative) BL-algebra [7]. Then, Turunen et al in [8,9] proved that -fold implicative BL-algebras are Gödel algebras, and -fold positive implicative BL-algebras are MV-algebras.…”

Some Types of Generalized Fuzzyn-Fold Filters in Residuated Lattices

“…One is the folding theory and the other is fuzzy sets theory. In the folding approach, in [9][10][11], -fold (positive) implicative filters are proposed in BL-algebras. In [12], -fold EIMTL and -fold IMTL-filters of MTL-algebras were defined and some relations between these filters andfold (positive) implicative filters, -fold fantastic filters, and -fold obstinate filters of MTL-algebras were investigated.…”