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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 Logic of graphs ： ウィキペディア英語版 Logic of graphs In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using logical formulas. There are several variations in the types of logical operation that can be used in these formulas. The first order logic of graphs concerns formulas in which the variables and predicates concern individual vertices and edges of a graph, while monadic second order graph logic allows quantification over sets of vertices or edges. A sentence $S$ may be true for some graphs, and false for others; a graph $G$ is said to ''model'' $S$, written $G\backslash models\; S$, if $S$ is true of the vertices and adjacency relation of $G$. The algorithmic problem of model checking concerns testing whether a given graph models a given sentence. The algorithmic problem of satisfiability concerns testing whether there exists a graph that models a given sentence. Although both model checking and satisfiability are hard in general, several major algorithmic meta-theorems show that properties expressed in this way can be tested efficiently for important classes of graphs. Other topics of research in the logic of graphs include investigations of the probability that a random graph has a property specified within a particular type of logic, and methods for data compression based on finding logical formulae that are modeled by a unique graph. ==First order== In the first-order logic of graphs, a graph property is expressed as a quantified logical formula whose variables represent graph vertices, with predicates for equality and adjacency testing. 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「Logic of graphs」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.