We present a new Priestley-style topological duality for bounded N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that for our topological ...

It is well-known that any substitution in intuitionistic propositional logic can be seen as an endomorphism between free Heyting algebras. For a given substitution σ : F (n)→ F (m), (where F (n) is the n-generated free Heyting algebra, n ∈ ω), the theory of σ is the filter σ−1(>). The theory of σ is finitely axiomatizable if σ−1(>) is a principal filter. The formula which generates this filter ...

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we define a new product on $Aoplus X$ and generalize the module extension Banach algebras. We  obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra.

A rough set logic based on Heyting-Brouwer algebras HBRSL is proposed as a basis for reasoning about rough information. It is an extension of Düntsch’s logic with intuitionistic implication, and is seen as a variant of HeytingBrouwer logic. A Kripke semantics and natural deduction for the logic are presented and the completeness theorem is proved.

some appropriate axioms (for details see [7]). These axioms imply that the relation ≈ on A defined by: a ≈ b if and only if a → b = 1 and b → a = 1, 1)/ ≈ is a Heyting algebra. For a given Heyting algebra B there always exists a Nelson algebra A such that A h is isomorphic to B: the Fidel-Vakarelov construction of the Nelson algebra N (B) (see e.g. [8]) yields an example of such an algebra. In ...

We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple desc...

Abstract This is the second of a series papers that investigate fragments quasi-Nelson logic (QNL) from an algebraic standpoint. QNL, recently introduced as common generalization intuitionistic and Nelson’s constructive with strong negation, axiomatic extension substructural $FL_{ew}$ (full Lambek calculus exchange weakening) by Nelson axiom. The counterpart QNL (quasi-Nelson algebras) class co...