Lattices and Boolean Algebra from Boole to Huntington to Shannon and Lattice Theory
نویسنده
چکیده
The study of computer design and architecture includes many topics on formal languages and discrete structures. Among these are state minimizations, Boolean algebra, and switching algebra. In minimization, three approaches are normally used that are based on equivalence relations. Partial order relations are used today in constructions of Boolean algebra. In this paper we survey this important algebra from its beginnings as alternative symbolic algebra starting with George Boole and De Morgan, to Peirce, to Venn, to Huntington and to Shannon. We then look at definitions based on lattice theory. Lattices are special cases of partially ordered sets that have common properties with equivalence relations. The paper is educational in nature intended to aid the instructor on this topic from its beginnings and provide a condensed survey.
منابع مشابه
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
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