About: Herbrand structure

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In first-order logic, a Herbrand structure S is a structure over a vocabulary σ that is defined solely by the syntactical properties of σ. The idea is to take the symbols of terms as their values, e.g. the denotation of a constant symbol c is just "c" (the symbol). It is named after Jacques Herbrand. Herbrand structures play an important role in the foundations of logic programming.

Attributes	Values
rdf:type	building
rdfs:label	Herbrand-Struktur (de) Herbrand structure (en) Estrutura de Herbrand (pt)
rdfs:comment	In first-order logic, a Herbrand structure S is a structure over a vocabulary σ that is defined solely by the syntactical properties of σ. The idea is to take the symbols of terms as their values, e.g. the denotation of a constant symbol c is just "c" (the symbol). It is named after Jacques Herbrand. Herbrand structures play an important role in the foundations of logic programming. (en) Em matemática, para uma linguagem , define o Universo de Herbrand para o conjunto de condições básicas de . Uma estrutura de é a Estrutura de Herbrand se o domínio de é o universo de Herbrand de e a interpretação de é a Interpretação de Herbrand. Isso corrige o domínio de , e de modo que cada Estrutura de Herbrand possa ser identificada com sua interpretação. Um Modelo de Herbrand de uma teoria é a estrutura de Herbrand que é um modelo de . (pt) Eine zu einer prädikatenlogischen Formelmenge F passende Struktur heißt Herbrand-Struktur, wenn folgende Eigenschaften erfüllt sind: * Das Universum ist das aus F generierte Herbrand-Universum, also . * Die Interpretationen I sind Herbrand-Interpretationen. Beispiel: Sei das Herbrand-Universum . Dann lautet die Zuordnung zwischen Funktionssymbolen und Elementen aus dem Universum: ... Herbrand-Strukturen werden im Satz von Herbrand verwendet und sind nach Jacques Herbrand benannt. (de)
dcterms:subject	Mathematical logic
Wikipage page ID	12274200 (xsd:integer)
Wikipage revision ID	1096525539 (xsd:integer)
Link from a Wikipage to another Wikipage	Resolution (logic) Skolem normal form Structure (mathematical logic) Logic programming First-order logic Ground term Herbrand's theorem Jacques Herbrand Term (logic) Mathematical logic Herbrand interpretation Herbrandization Springer Science+Business Media Signature (logic)
Link from a Wikipage to an external page	https://archive.org/details/mathematicallogi1996ebbi
sameAs	Herbrand structure Herbrand structure Herbrand structure Herbrand structure Herbrand structure Herbrand structure
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_book dbt:I_sup dbt:Math dbt:Mvar dbt:Short_description dbt:Sup dbt:Olist dbt:Mset
has abstract	Eine zu einer prädikatenlogischen Formelmenge F passende Struktur heißt Herbrand-Struktur, wenn folgende Eigenschaften erfüllt sind: * Das Universum ist das aus F generierte Herbrand-Universum, also . * Die Interpretationen I sind Herbrand-Interpretationen. Bei einer Interpretation werden den Funktions- und Konstantensymbolen tatsächliche Funktionen und Konstanten zugeordnet. Bei der Herbrand-Interpretation weist man jedem Funktionsterm eine Interpretation durch sich selbst zu. Dies ist möglich, da das Herbrand-Universum genau aus der Menge aller möglichen Terme mit Funktions- und Konstantensymbolen besteht. Damit ist eine Herbrand-Struktur eine Terminterpretation. Beispiel: Sei das Herbrand-Universum . Dann lautet die Zuordnung zwischen Funktionssymbolen und Elementen aus dem Universum: ... Herbrand-Strukturen werden im Satz von Herbrand verwendet und sind nach Jacques Herbrand benannt. (de) In first-order logic, a Herbrand structure S is a structure over a vocabulary σ that is defined solely by the syntactical properties of σ. The idea is to take the symbols of terms as their values, e.g. the denotation of a constant symbol c is just "c" (the symbol). It is named after Jacques Herbrand. Herbrand structures play an important role in the foundations of logic programming. (en) Em matemática, para uma linguagem , define o Universo de Herbrand para o conjunto de condições básicas de . Uma estrutura de é a Estrutura de Herbrand se o domínio de é o universo de Herbrand de e a interpretação de é a Interpretação de Herbrand. Isso corrige o domínio de , e de modo que cada Estrutura de Herbrand possa ser identificada com sua interpretação. Um Modelo de Herbrand de uma teoria é a estrutura de Herbrand que é um modelo de . (pt)
gold:hypernym	Structure
prov:wasDerivedFrom	wikipedia-en:Herbrand_structure?oldid=1096525539&ns=0
page length (characters) of wiki page	4535 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Herbrand_structure
is Link from a Wikipage to another Wikipage of	Inductive logic programming List of mathematical logic topics Gisbert Hasenjaeger Herbrand's theorem Jacques Herbrand Herbrand interpretation Term model Scientific phenomena named after people Herbrand's theorem Minimal Herbrand model Herbrand base Herbrand model
is Wikipage redirect of	Term model Herbrand's theorem Minimal Herbrand model Herbrand base Herbrand model
is foaf:primaryTopic of	wikipedia-en:Herbrand_structure

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