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1.2 Models

For a many-sorted signature Sigma= (S,TF,PF,P) a  many-sorted model M e Mod(Sigma) is a  many-sorted first-order structure consisting of a  many-sorted partial algebra:

together with:

A (weak)  many-sorted homomorphism h from M1 to M2, with M1, M2 e Mod(S,TF,PF,P), consists of a function hs:sM1 -> sM2 for each s e S preserving not only the values of functions but also their definedness, and preserving the truth of predicates.

Any signature morphism sigma:Sigma -> Sigma' determines the  many-sorted reduct of each model M' e Mod(Sigma') to a model M e Mod(Sigma), defined by interpreting symbols of Sigma in M in the same way that their images under sigma are interpreted in M'.

CoFI Document: CASL/Summary-v1.0 -- Version: 1.0 -- 22 October 1998.
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