A note on residuated po-groupoids and lattices with antitone involutions

TL;DR

This paper explores the relationships between left-residuated po-groupoids and basic algebras, extending the understanding of non-commutative, non-associative algebraic structures related to logic.

Contribution

It clarifies the connections between residuated structures and basic algebras, generalizing previous work on algebraic frameworks for logic.

Findings

Established links between residuated po-groupoids and basic algebras.

Extended the theory of non-commutative, non-associative algebraic structures.

Provided insights into the algebraic foundations of certain logical systems.

Abstract

Following [Botur, M., Chajda, I., Hala\v{s}, R.: Are basic algebras residuated structures?, Soft Comput. 14 (2010), 251-255] we discuss the connections between left-residuated partially ordered groupoids and the so-called basic algebras, which are a non-commutative and non-associative generalization of MV-algebras and orthomodular lattices.