Correspondences

Language

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

Model

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

 

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