Reduced axioms for the propositional logics induced by basic algebras

Abstract

A certain logic induced by basic algebras was already studied by the first author in Chajda (Int J Theor Phys 54:4306–4312, 2015) and, for the particular case of the so-called commutative basic algebras, axiom system was established by Botur and Halas (Arch Math Logic 48:243–255, 2009). In Kolařik (Discuss Math Gen Algebra Appl 36:113–116, 2016) the just mentioned axiom system was essentially reduced. The aim of this paper is to reduce the original axiom system from Chajda (Int J Theor Phys 54:4306–4312, 2015) and to show that it is the best possible reduction in the sense that the remaining axioms are independent.