Generalizations of Implication Algebras
msra（2007）
摘要
Implication algebras, originally introduced in order to study algebraic properties of the implication operation in Boolean algebras, are generalized and it is shown that these more general algebras are in one-to-one correspondence to semilattices with 1 the principal filters of which are posets with an antitone involution, respectively to commutative directoids with 1 the principal filters of which are posets with a switching involution.
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关键词
boolean algebra,poset,orthomodular lattice,weak i-algebra,switching involution.,antitone involution,orthoimplication algebra,semilattice,orthomodular implication algebra,implication algebra,directoid,strong i-algebra
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