Quasi-orthomodular posets and weak BCK-algebras.
A \textit{weak BCK-algebra} (wBCK-algebra for short) is an algebra \((A,-,0)\), where \(A\) is a poset with \(0\) the least element, and \(-\) a total binary operation on \(A\) (called subtraction) satisfying the following axioms: (1) \(x\leq y\) iff \(x-y=0\), and (2) if \(x-y\leq z\), then \(x-z\leq y\). This notion generalizes BCK-algebra. The author is studying orthomodular-type posets (quasi-orthomodular ones, etc.), semilattices, nearlattices and lattices, and compares with each other and with wBCK-algebras.
scientific article; zbMATH DE number 6363133
scientific article