Algebras of logic as BCK algebras

This monograph collects the principal results, published or not yet published, obtained by the author in the last six years, in the attempt to treat unitarily some commutative algebras of logic (Boolean algebras, residuated lattices, Hilbert algebras, MV algebras, divisible residuated lattices, Heyting algebras, BCK-algebras, Wajsberg algebras, BL algebras, Gödel algebras, Product algebras, (weak-) Ro algebras, MTL algebras, WNM algebras, IMTL algebras, NM algebras) and the corresponding non-commutative algebras of logic (non-commutative residuated lattices, pseudo-MV algebras, divisible non-commutative residuated lattices, pseudo-BCK algebras, pseudo-Wajsberg algebras, pseudo-BL algebras, pseudo-Product algebras, (weak-) pseudo-Ro algebras, pseudo-MTL algebras, pseudo-WNM algebras, pseudo-IMTL algebras, pseudo-NM algebras), as particular cases of reversed left-BCK algebras and reversed left-pseudo-BCK algebras, respectively, in order to be closer to logic. Note that Boolean algebras, Hilbert algebras, Heyting algebras and Gödel algebras cannot be generalized to the non-commutative case.

There are two main groups of intended readers. First, students at master and Ph.D studies in algebra of logic and computer science. Second, equally important, researchers involved in algebra of logic and computer science.