About: Finite model theory

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Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe.

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rdfs:label	Finite model theory (en) Théorie des modèles finis (fr) 有限モデル理論 (ja) Teoria de modelos finitos (pt)
rdfs:comment	La théorie des modèles finis est un sous-domaine de la théorie des modèles. Cette dernière est une branche de la logique mathématique qui traite de la relation entre un langage formel (la syntaxe) et ses interprétations (ses sémantiques). La théorie des modèles finis est la restriction de la théorie des modèles aux interprétations de structures finies, donc qui sont définies sur un ensemble (un univers) fini. Ses applications principales sont la théorie des bases de données, la complexité descriptive et la théorie des langages formels. (fr) Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe. (en) 有限モデル理論（英: Finite model theory）とは、モデル理論の一種であり、一階述語論理などの論理言語を有限構造（有限群、グラフ、データベース、多くの計算模型など）に適用したときの属性に着目した理論である。論理言語と計算の関係に特に注目し、離散数学や計算複雑性理論やとも密接に関連する。一階述語論理と古典モデル理論の重要な成果の多くは、有限構造に制限されると成り立たない。例えば、コンパクト性定理、クレイグの補間定理、レーヴェンハイム-スコーレムの定理、ゲーデルの完全性定理などである。このような文脈では、一階述語論理の表現能力が十分とは言えない点が根本的な問題である。このため、一階述語論理に推移閉包や最小不動点の作用素を追加したり、二階述語論理の一部を使ったりして、有限構造での属性を表現できる新たな論理体系を構築する。有限モデル理論では、論理の有限な制限についても研究する。例えば、変項数を k 個に制限された一階述語論理などである。 (ja) Teoria dos modelos finitos (TMF) é uma subárea da Teoria dos modelos (TM). A TM é um ramo da Lógica matemática que lida com a relação entre a linguagem formal (sintaxe) e suas interpretações (semântica). A TMF é uma restrição da TM para a interpretação de estruturas que tem um universo finito. (pt)
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dcterms:subject	Finite model theory Model theory
Wikipage page ID	1773596 (xsd:integer)
Wikipage revision ID	1124277712 (xsd:integer)
Link from a Wikipage to another Wikipage	Model theory NP (complexity) Relational algebra Finite model theory Descriptive Complexity Interpretation (logic) PSPACE-complete SQL Prenex normal form Trakhtenbrot's theorem Quantifier rank Moshe Vardi NL (complexity) L (complexity) Logic Logic of graphs Löwenheim–Skolem theorem Compactness theorem Complexity class Computational problem PH (complexity) P (complexity) Propositional logic Structure (mathematical logic) Transitive closure Database theory Domain relational calculus Gödel's completeness theorem Heinz-Dieter Ebbinghaus Least fixed point Non-standard model of arithmetic Addison-Wesley First-order logic Formal language Existential second-order logic Quantifier (logic) Query (complexity) Heinrich Scholz Abstract algebra Abstract machine Model theory Codd's theorem Ehrenfeucht–Fraïssé game Springer Science+Business Media Second-order logic Serge Abiteboul Neil Immerman Victor Vianu Fagin's theorem Immerman–Szelepcsényi theorem Nonfirstorderizability Ultraproduct SQL:1999 Least fixed-point logic Springer-Verlag Logical system Fixpoint logic Almost always Descriptive complexity Recursive WITH
Link from a Wikipage to an external page	https://archive.org/details/foundationsofdat0000abit https://www.springer.com/cda/content/document/cda_downloaddocument/9783540212027-c1.pdf http://www-mgi.informatik.rwth-aachen.de/FMT/index.html.en http://www.math.helsinki.fi/logic/people/jouko.vaananen/shortcourse.pdf https://archive.org/details/elementsoffinite00libk https://web.archive.org/web/20120717064043/http:/www-mgi.informatik.rwth-aachen.de/FMT/index.html.en https://web.archive.org/web/20150924123212/http:/www.springer.com/cda/content/document/cda_downloaddocument/9783540212027-c1.pdf http://homepages.inf.ed.ac.uk/libkin/papers/fmtpods09.pdf http://www.cl.cam.ac.uk/~ad260/modth/slides.pdf
sameAs	Finite model theory Finite model theory Finite model theory Finite model theory Finite model theory Finite model theory
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