논문KCI 등재
Remarks on the Valid Equations in Lattice Implication Algebras
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Abstract
We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.
관련 논문AI추천
On fuzzy implicative filters of lattice implication algebrasEun Hwan Roh$, Qun Zhang, Yiquan Zhu대한수학회 · 대한수학회논문집2003 · 제18권 제4호The Condition under Which a Pre-logic Becomes an Implication AlgebraIvan Chajda경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제2호Topological aspects of filters in lattice implication algebras전영배대한수학회 · 대한수학회보2006 · 제43권 제2호Algebraic semantics for some weak Boolean logics양은석한국논리학회 · 논리연구2006 · 제9권 제2호Weak Distributive n-Semilattices and n-Lattices임선주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제2호Folding theory of implicative/fantastic filters in lattice implication algebrasSeok Zun Song, Young Bae Jun대한수학회 · 대한수학회논문집2004 · 제19권 제1호
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