Paraconsistent and Paracomplete Logics Based on k-Cyclic Modal Pseudocomplemented De Morgan Algebras

A note on k-cyclic modal pseudocomplemented De Morgan algebras

“…Then, we have the following Lemma: Lemma 2.4 [11] Let (A, t) be a C k -algebra, P ⊆ A a prime filter, and ϕ is the Birula-Rasiowa transformation on A. Then, the following properties hold:…”

“…In what follows, we will present important examples of C k -algebra, in fact, as we will see they are the generating algebra of the variety. Remark 2.6 [11] Let T 2 , T 3 , and T 4 be the simple algebras of the variety of mpMalgebras, see Remark 2.2. In the following, we will consider the sets T 2,k , T 3,k , and 3, 4) and with the pointwise defined operations.…”

“…Theorem 2.9 [11] The variety of C k -algebras is finitely generated and locally finite. Besides, the only simple algebras are T i,k = (T i,k , t) with i = 3, 4 and their subalgebras.…”

“…It is worth mentioning that the class of mpM −algebras constitutes a proper subvariety of the variety V 0 studied by H. Sankappanavar in [23]. More recently, the theory of operators over mpM −algebras was considered by Figallo-Orellano et al in [10,11,12]. In particular, they studied the class of mpM −algebras enriched with an automorphism of period 2 and k, where k is an positive integer; in fact, this automorphism works as a new unary operator.…”

“…In particular, they studied the class of mpM −algebras enriched with an automorphism of period 2 and k, where k is an positive integer; in fact, this automorphism works as a new unary operator. Recently, the class of k-cyclic mpM -algebras has been related with paraconsistent logics and logics formal inconsistency (LFIs, see [5]) through degree-preserving construction in [11]; clearly, when we take k = 2, we obtain the class of symmetric mpMalgebras. On the other hand, monadic and modal operators over special Heyting algebras were studied in [1,6,20].…”