On BCK Algebras - Part I.a: An Attempt to Treat Unitarily the Algebras of Logic. New Algebras

: 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” algebras. In some circumstances, this choice is essential, for instance if we want to build the ordinal sum (product) between a BL algebra and an MV algebra. We have chosen the ”left” presentation and several algebras of logic have been redefined as particular cases of BCK algebras. We introduce several new properties of algebras of logic, besides those usually existing in the literature, which generate a more refined classification, depending on the properties satisfied. In this work (Parts I-V) we make an exhaustive study of these algebras - with two bounds and with one bou...

• Type: Journal
• Year: 2007
• Where: JUCS
• Authors: Afrodita Iorgulescu
• Keywords: Algebra, Associated Order Relation, JUCS 2007, Presentation