Implication algebras

• Autorzy: Ivan Chajda
• Języki publikacji: EN

Abstrakty

EN

We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties.

Słowa kluczowe

EN

implication algebra; pre-implication algebra; orthoimplication algebra; orthosemilattice; congruence kernel

Kategorie tematyczne

• 06C15: Complemented lattices, orthocomplemented lattices and posets
• 08B10: Congruence modularity, congruence distributivity
• 03G25: Other algebras related to logic
• 08A30: Subalgebras, congruence relations
• 03G12: Quantum logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 141-153

Daty

wydano

2006

otrzymano

2005-01-10

poprawiono

2006-03-29

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [1] J.C. Abbott, Semi-Boolean algebra, Matem. Vestnik 4 (1967), 177-198.
• [2] J.C. Abbott, Orthoimplication Algebras, Studia Logica 35 (1976), 173-177.
• [3] L. Beran, Orthomodular Lattices, Algebraic Approach, Mathematic and its Applications, D. Reidel Publ. Comp., 1985.
• [4] I. Chajda and R. Halaš, An Implication in Orthologic, submitted to Intern. J. Theor. Phys. 44 (2006), 735-744.
• [5] I. Chajda, R. Halaš and H. Länger, Orthomodular implication algebras, Intern. J. Theor. Phys. 40 (2001), 1875-1884.
• [6] G.M. Hardegree, Quasi-implication algebras, Part I: Elementary theory, Algebra Universalis 12 (1981), 30-47.
• [7] G.M. Hardegree, Quasi-implication algebras, Part II: Sructure theory, Algebra Universalis 12 (1981), 48-65.
• [8] J. Hedliková, Relatively orthomodular lattices, Discrete Math., 234 (2001), 17-38.
• [9] M.F. Janowitz, A note on generalized orthomodular lattices, J. Natural Sci. Math. 8 (1968), 89-94.
• [10] N.D. Megill and M. Pavičić, Quantum implication algebras, Intern. J. Theor. Phys. 48 (2003), 2825-2840.

Identyfikatory

DOI

10.7151/dmgaa.1108