Endowing a lower-bounded partially ordered set with a total addition or with a total difference operation leads to the basic notion of a NAM, that is, a naturally ordered abelian monoid, or a BCK-algebra, respectively. BL-algebras may be alteratively viewed as certain NAMs or certain BCK-algebras. We characterize the appropriate subclasses by making use of those properties which have been so fa...

We study hyper pseudo BCC-algebras which are a common generalization of and BCK-algebras. In particular, we introduce different notion describe the relationship among them. Then, by choosing one these definitions, investigate for its related properties.

A symplified axiomatization of pseudo-BCK algebras is given. In addition, we obtain a system of axioms defining bounded commutative pseudoBCK algebras and show that these axioms are independent (that is, none follows from the others). 2010 Mathematics Subject Classification: 03G25, 06F05, 06F35

In this paper, we have studied the notion of nearness $d$-algebras which is a generalization BCK-algebras (or NBCK-algebra for short). Therefore, it defined that notions d$-subalgebra, d-ideal in $d$-algebras. Afterward, investigated relations among them and gave some examples.

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...

The notion of a positive implicative pseudo-valuation on a BCKalgebra is introduced, and its characterizations are investigated. The relationship between a pseudo-valuation and a positive implicative pseudovaluation is examined. Reduction property for a positive implicative pseudo-valuation is established. Mathematics Subject Classification: 06F35, 03G25