翻訳と辞書 Words near each other ・ Cylindera paludosa ・ Cylinders of Nabonidus ・ Cylindilla ・ Cylindilla bidentata ・ Cylindilla formosana ・ Cylindilla grisescens ・ Cylindilla inornata ・ Cylindilla interrupta ・ Cylindilla makiharai ・ Cylindilla parallela ・ Cylindracanthus ・ Cylindraspis ・ Cylindrecamptus lineatus ・ Cylindrellinidae ・ Cylindrepomus ・ Cylindric algebra ・ Cylindric numbering ・ Cylindrical algebraic decomposition ・ Cylindrical coordinate system ・ Cylindrical drum ・ Cylindrical equal-area projection ・ Cylindrical grinder ・ Cylindrical harmonics ・ Cylindrical joint ・ Cylindrical lanternshark ・ Cylindrical lens ・ Cylindrical lioplax ・ Cylindrical multipole moments ・ Cylindrical perspective ・ Cylindrical σ-algebra Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cylindric algebra ： ウィキペディア英語版 Cylindric algebra The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic with equality. This is comparable to the role Boolean algebras play for propositional logic. Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification and equality. They differ from polyadic algebras in that the latter do not model equality. == Definition of a cylindric algebra == A cylindric algebra of dimension $\backslash alpha$ (where $\backslash alpha$ is any ordinal number) is an algebraic structure $(A,+,\backslash cdot,-,0,1,c\_\backslash kappa,d\_)\_$ such that $(A,+,\backslash cdot,-,0,1)$ is a Boolean algebra, $c\_\backslash kappa$ a unary operator on $A$ for every $\backslash kappa$, and $d\_$ a distinguished element of $A$ for every $\backslash kappa$ and $\backslash lambda$, such that the following hold: (C1) $c\_\backslash kappa\; 0=0$ (C2) $x\backslash leq\; c\_\backslash kappa\; x$ (C3) $c\_\backslash kappa(x\backslash cdot\; c\_\backslash kappa\; y)=c\_\backslash kappa\; x\backslash cdot\; c\_\backslash kappa\; y$ (C4) $c\_\backslash kappa\; c\_\backslash lambda\; x=c\_\backslash lambda\; c\_\backslash kappa\; x$ (C5) $d\_=1$ (C6) If $\backslash kappa\backslash notin\backslash$, then $d\_=c\_\backslash kappa(d\_\backslash cdot\; d\_)$ (C7) If $\backslash kappa\backslash neq\backslash lambda$, then $c\_\backslash kappa(d\_\backslash cdot\; x)\backslash cdot\; c\_\backslash kappa(d\_\backslash cdot\; -x)=0$ Assuming a presentation of first-order logic without function symbols, the operator $c\_\backslash kappa\; x$ models existential quantification over variable $\backslash kappa$ in formula $x$ while the operator $d\_$ models the equality of variables $\backslash kappa$ and $\backslash lambda$. Henceforth, reformulated using standard logical notations, the axioms read as (C1) $\backslash exists\; \backslash kappa.\; \backslash mathit\; \backslash Leftrightarrow\; \backslash mathit$ (C2) $x\; \backslash Rightarrow\; \backslash exists\; \backslash kappa.\; x$ (C3) $\backslash exists\; \backslash kappa.\; (x\backslash wedge\; \backslash exists\; \backslash kappa.\; y)\; \backslash Leftrightarrow\; (\backslash exists\backslash kappa.\; x)\; \backslash wedge\; (\backslash exists\backslash kappa.\; y)$ (C4) $\backslash exists\backslash kappa\; \backslash exists\backslash lambda.\; x\; \backslash Leftrightarrow\; \backslash exists\; \backslash lambda\; \backslash exists\backslash kappa.\; x$ (C5) $\backslash kappa=\backslash kappa\; \backslash Leftrightarrow\; \backslash mathit$ (C6) If $\backslash kappa$ is a variable different from both $\backslash lambda$ and $\backslash mu$, then $\backslash lambda=\backslash mu\; \backslash Leftrightarrow\; \backslash exists\backslash kappa.\; (\backslash lambda=\backslash kappa\; \backslash wedge\; \backslash kappa=\backslash mu)$ (C7) If $\backslash kappa$ and $\backslash lambda$ are different variables, then $\backslash exists\backslash kappa.\; (\backslash kappa=\backslash lambda\; \backslash wedge\; x)\; \backslash wedge\; \backslash exists\backslash kappa.\; (\backslash kappa=\backslash lambda\backslash wedge\; \backslash neg\; x)\; \backslash Leftrightarrow\; \backslash mathit$ 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「Cylindric algebra」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.