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Keywords:
orthoimplication algebra; orthomodular lattice; $p$-filter
orthoimplication algebra; orthomodular lattice; $p$-filter
Summary:
Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.
References:
[1] Abbott, J. C.: Semi-boolean algebra. Mat. Vestnik 4 (1967), 177–198. MR 0239957 | Zbl 0153.02704
[2] Abbott, J. C.: Orthoimplication algebras. Stud. Log. 35 (1976), 173–177. DOI 10.1007/BF02120879 | MR 0441794 | Zbl 0331.02036
[3] Beran, L.: Orthomodular Lattices—Algebraic Approach. D. Reidel, Dordrecht, 1985. MR 0784029 | Zbl 0558.06008
[4] Burmeister, P., Maczyński, M.: Orthomodular (partial) algebras and their representations. Demonstr. Math. 27 (1994), 701–722. MR 1319415
[5] Chajda I., Halaš, R., Kühr, J.: Implication in MV-algebras. Algebra Univers. 52 (2004), 377–382. MR 2120523
[6] Chajda I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions. Acta Sci. (Szeged) 71 (2005), 19–33. MR 2160352
[7] Chajda, I., Halaš, R., Länger, H.: Orthomodular implication algebras. Int. J. Theor. Phys. 40 (2001), 1875–1884. DOI 10.1023/A:1011933018776 | MR 1860644
[8] Chajda, I., Halaš, R., Länger, H.: Simple axioms for orthomodular implication algebras. Int. J. Theor. Phys. 40 (2004), 911–914. DOI 10.1023/B:IJTP.0000048587.50827.93 | MR 2106354
[9] Halaš, R.: Ideals and D-systems in Orthoimplication algebras. J. Mult.-Val. Log. Soft Comput. 11 (2005), 309–316. MR 2160472 | Zbl 1078.03050
[10] Kalmbach, G.: Orhomodular Lattices. Academic Press, London, 1983. MR 0716496
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