s0 = I1 and G1 ⊆ sn. Then there is a path t0, t1, . . . , tn in G(P2) such that t0 = I2 and si
=1 for all i (0 ≤ i ≤ n), and 
it follows that G2 ⊆ tn. This means that a solution path for a speciﬁc instance can always be weakly upwards reﬁned into 
a corresponding abstract solution. It could, thus, make sense to also consider variants of our properties that apply only to 
speciﬁc instances. Such properties should not replace the ones deﬁned in this article, but rather complement them. A similar 
case arises for admissibility of heuristics, which is deﬁned to hold for all paths in the instance, disregarding speciﬁc initial 
states and goals. The idea of globally admissible heuristics [62] restricts the concept such that admissibility only needs to 
hold for speciﬁc paths, which is similar to the suggestion above of adding a restricted case of reﬁnability.
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