Semilattice implication algebras
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We define a logical system, semilattice implication algebra, for a generalization of lattice implication algebras and Heyting semilattices and research some properties of this algebra, and the regular element in a semilattice implication algebra is defined and it is porved that the set of all regular elements is a distributive lattice. Also, we give some relationships of filters and multipliers, and give a filter constructed by a subsemigroup of monotone multipliers. And then it is showed that the filter generated by a subset is charaterized by simple multipliers.
Abstract
We define a logical system, semilattice implication algebra, for a generalization of lattice implication algebras and Heyting semilattices and research some properties of this algebra, and the regular element in a semilattice implication algebra is defined and it is porved that the set of all regular elements is a distributive lattice. Also, we give some relationships of filters and multipliers, and give a filter constructed by a subsemigroup of monotone multipliers. And then it is showed that the filter generated by a subset is charaterized by simple multipliers.
참고문헌 (15)
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