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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Vector logic ： ウィキペディア英語版 Vector logic Vector logic〔Mizraji, E. (1992). (Vector logics: the matrix-vector representation of logical calculus. ) Fuzzy Sets and Systems, 50, 179–185, 1992〕〔Mizraji, E. (2008) (Vector logic: a natural algebraic representation of the fundamental logical gates. ) Journal of Logic and Computation, 18, 97–121, 2008〕 is an algebraic model of elementary logic based on matrix algebra. Vector logic assumes that the truth values map on vectors, and that the monadic and dyadic operations are executed by matrix operators. == Overview == Classic binary logic is represented by a small set of mathematical functions depending on one (monadic ) or two (dyadic) variables. In the binary set, the value 1 corresponds to ''true'' and the value 0 to '' false''. A two-valued vector logic requires a correspondence between the truth-values ''true'' (t) and ''false'' (f), and two ''q''-dimensional normalized column vectors composed by real numbers ''s'' and ''n'', hence: : $t\backslash mapsto\; s$    and    $f\backslash mapsto\; n$ (where $q\; \backslash geq\; 2$ is an arbitrary natural number, and “normalized” means that the length of the vector is 1; usually s and n are orthogonal vectors). This correspondence generates a space of vector truth-values: ''V''2 = . The basic logical operations defined using this set of vectors lead to matrix operators. The operations of vector logic are based on the scalar product between ''q''-dimensional column vectors: $u^Tv=\backslash langle\; u,v\backslash rangle$: the orthonormality between vectors ''s'' and ''n'' implies that $\backslash langle\; u,v\backslash rangle=1$ if $u\; =\; v$, and $\backslash langle\; u,v\backslash rangle=0$ if $u\; \backslash ne\; v$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vector logic」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.