Displaying similar documents to “The axioms for implication in orthologic”

On systems of congruences on principal filters of orthomodular implication algebras

Radomír Halaš, Luboš Plojhar (2007)

Mathematica Bohemica

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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.

Implication and equivalential reducts of basic algebras

Ivan Chajda, Miroslav Kolařík, Filip Švrček (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A term operation implication is introduced in a given basic algebra 𝒜 and properties of the implication reduct of 𝒜 are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of 𝒜 and, if this partial order is linear, the algebra 𝒜 can be reconstructed...