Correspondences

Language

 

Text Box: IFF	Mathematics	
<Language id=L>	L = rel(L), ent(L), 	declaration of a language
extends	inc, inc : L  L	language morphism
<Entity typ=α>	α  ent(L)	declaration of an entity type
<Relation typ=ρ>	ρ  rel(L)	declaration of a relation type
argument	x : rel(L)  ent(L), x  varρ : var  ent(L), ρ  rel(L)	signature of a relation type
    argument.index	x  arity(ρ)	variable (participant) in the arity
    argument.entType	ρ(x)  rel(L)	entity type in the signature

Model

Text Box: IFF	Mathematics	
<Model id=A lang=L>	A = rel(A), ent(A), )  Model(L)	declaration of a model
<Classification kind=ent>	ent(A) = inst.ent(A), typ.ent(A), ⊨A	entity classification of a model
<Classification kind=rel>	rel(A) = inst.rel(A), typ.rel(A), ⊨A	relation classification of a model
<α id=a about =  >  </α>	a ⊨ αa  inst.ent(A) and α  typ.ent(A) 	assertion of an entity instanceand an entity classification
<ρ>  <x1 val=a1/>    <xn val=an/>  </ρ>	t ⊨ ρt  inst.rel(A) and ρ  typ.rel(A)where (t) = a 	assertion of a relation instanceand a relational classification

 

Please send questions, comments and suggestions about this page to: Robert E. Kent rekent@ontologos.org

Copyright 2000 TOC (The Ontology Consortium). All rights reserved. Revised: July 2000

 

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