Extensions of the Language: Structures

Abstract

Instead of considering just one relation, we could consider the structure formed by a finite set of relations R 1,…, R k , of arities m 1,…,m k , respectively, all on the same universe E; such a structure is called a multirelation; the sequence of arities m 1,…,m k is called the signature (or similarity type) of the multirelation. Given a second multirclation (S 1,…, S k ) with universe F and the same signature, an isomorphism from (R 1,…, R k ) to (S 1,…, S k ) is a function s from E to F that is an isomorphism from R 1 to S 1,…, from R k to S k . The notions of extension, embedding, local isomorphism, p-isomorphism, etc. are defined the same way as for relations. For the language associated with a multirelation, or more precisely with its signature, we now must introduce k relation symbols, instead of just one: one of arity m 1 to denote R 1, …, one of arity m k to denote R k .KeywordsFunction SymbolAtomic FormulaRelation SymbolConstant SymbolBibliographic NoteThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.