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- Term_algebra abstract "In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X. Other synonyms for the notion include absolutely free algebra, anarchic algebra.From a category theory perspective, a term algebra is the initial object for the category of all algebras of the same signature, and this object, unique up to isomorphism is called an initial algebra; it generates by homomorphic projection all algebras in the category.A similar notion is that of a Herbrand universe in logic, usually used under this name in logic programming, which is (absolutely freely) defined starting from the set of constants and function symbols in a set of clauses. That is, the Herbrand universe consists of all ground terms: terms that have no variables in them.An atomic formula or atom is commonly defined as a predicate applied to a tuple of terms; a ground atom is then a predicate in which only ground terms appear. The Herbrand base is the set of all ground atoms that can be formed from predicate symbols in the original set of clauses and terms in its Herbrand universe.These two concepts are named after Jacques Herbrand.Term algebras also play a role in the semantics of abstract data types, where an abstract data type declaration provides the signature of a multi-sorted algebraic structure and the term algebra is a concrete model of the abstract declaration.".
- Term_algebra wikiPageExternalLink structure-free.pdf.
- Term_algebra wikiPageID "2216678".
- Term_algebra wikiPageLength "5902".
- Term_algebra wikiPageOutDegree "37".
- Term_algebra wikiPageRevisionID "702279872".
- Term_algebra wikiPageWikiLink Abstract_data_type.
- Term_algebra wikiPageWikiLink Algebraic_structure.
- Term_algebra wikiPageWikiLink Answer_set_programming.
- Term_algebra wikiPageWikiLink Atomic_formula.
- Term_algebra wikiPageWikiLink Binary_operation.
- Term_algebra wikiPageWikiLink Binary_tree.
- Term_algebra wikiPageWikiLink Category:Free_algebraic_structures.
- Term_algebra wikiPageWikiLink Category:Mathematical_logic.
- Term_algebra wikiPageWikiLink Category:Universal_algebra.
- Term_algebra wikiPageWikiLink Category_theory.
- Term_algebra wikiPageWikiLink Clause_(logic).
- Term_algebra wikiPageWikiLink Clone_(algebra).
- Term_algebra wikiPageWikiLink Domain_of_discourse.
- Term_algebra wikiPageWikiLink F-algebra.
- Term_algebra wikiPageWikiLink Ground_expression.
- Term_algebra wikiPageWikiLink Herbrand_interpretation.
- Term_algebra wikiPageWikiLink Herbrand_structure.
- Term_algebra wikiPageWikiLink Homomorphism.
- Term_algebra wikiPageWikiLink Infinite_tree_automaton.
- Term_algebra wikiPageWikiLink Initial_algebra.
- Term_algebra wikiPageWikiLink Initial_and_terminal_objects.
- Term_algebra wikiPageWikiLink Jacques_Herbrand.
- Term_algebra wikiPageWikiLink Logic.
- Term_algebra wikiPageWikiLink Logic_programming.
- Term_algebra wikiPageWikiLink Magma_(algebra).
- Term_algebra wikiPageWikiLink Mathematical_logic.
- Term_algebra wikiPageWikiLink Nonelementary_problem.
- Term_algebra wikiPageWikiLink Predicate_(mathematical_logic).
- Term_algebra wikiPageWikiLink Quantifier_elimination.
- Term_algebra wikiPageWikiLink Semantics.
- Term_algebra wikiPageWikiLink Signature_(logic).
- Term_algebra wikiPageWikiLink Universal_algebra.
- Term_algebra wikiPageWikiLink Universe_(mathematics).
- Term_algebra wikiPageWikiLinkText "Term algebra".
- Term_algebra wikiPageWikiLinkText "Terms".
- Term_algebra wikiPageWikiLinkText "term algebra".
- Term_algebra wikiPageWikiLinkText "terms".
- Term_algebra title "Herbrand Universe".
- Term_algebra urlname "HerbrandUniverse".
- Term_algebra wikiPageUsesTemplate Template:Mathworld.
- Term_algebra wikiPageUsesTemplate Template:Refbegin.
- Term_algebra wikiPageUsesTemplate Template:Refend.
- Term_algebra wikiPageUsesTemplate Template:Reflist.
- Term_algebra subject Category:Free_algebraic_structures.
- Term_algebra subject Category:Mathematical_logic.
- Term_algebra subject Category:Universal_algebra.
- Term_algebra type Field.
- Term_algebra type Redirect.
- Term_algebra type Structure.
- Term_algebra comment "In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X.".
- Term_algebra label "Term algebra".
- Term_algebra sameAs Q21998744.
- Term_algebra sameAs Termalgebra.
- Term_algebra sameAs m.06wnzj.
- Term_algebra sameAs Q21998744.
- Term_algebra wasDerivedFrom Term_algebra?oldid=702279872.
- Term_algebra isPrimaryTopicOf Term_algebra.