BCK Algebras versus m-BCK Algebras. Foundations

<p><br></p><p>This monograph gathers the author's results obtained since April 2019 which have been published in seven papers. Starting from the</p><p>frame-work centered on BCK algebras m-BCK algebras are defi ned ('m' coming from 'magma') (algebras including the MV and the</p><p>Boolean algebras) and other more general algebras thus obtaining an analogous new frame-work centered on m-BCK algebras.</p><p>'Bridge theorems' connecting the two frameworks are obtained in the involutive case.</p><p><br></p><p>Incorporated within this new frame-work are the quantum structures: the bounded involutive lattices the De Morgan algebras</p><p>the ortholattices the quantum MV algebras the orthomodular lattices with important new results and many examples obtained by using</p><p>the computer program Prover9/Mace4. Also included in the book are some new results never published before on L algebras on quantum B</p><p>algebras pseudo-BCI/pseudo-BCK algebras and prealgebras (in the non-commutative case) and important final results on quantum structures</p><p>with many examples.</p><p><br></p><p>This monograph has 17 chapters divided into three parts: Part I focuses on the 'world' of BCK algebras and of pseudo-BCK algebras</p><p>Part II concentrates on the 'world' of m-BCK algebras and Part III is about 'bridge theorems' between the two 'worlds'.</p>