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C. Bäckström and P. Jonsson

Artiﬁcial Intelligence 302 (2022) 103608

holds both upward and downward. For instance, C(cid:14) (up-down coupled) means that both C↑ and C↓ hold. These classiﬁcations 
retain the symmetric nature of transformations. For instance, (cid:3) f , R(cid:4) is a C↓ transformation from G1 to G2 if and only if 
(cid:3) f , R(cid:4) is  a  C↑ transformation  from  G2 to  G1.  It  should  be  noted  that  these  properties  are  only  examples  that  we  have 
chosen to use in this paper since they are simple, yet powerful. It is naturally possible to deﬁne other similar properties 
within our framework.
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen