I don’t think this terminology is really helping any more? Everything other than a full linearisation doesn’t really sound very linear anymore. As it stands, {\emptyset, ABC} would be called a linearisation even though it does nothing to put the elements A,B,C in a line or an order, eg. Something like “escalating grouping” seems clearer: that is you select some groups of transactions, such that you can order them so that every group earlier than g is a proper subset of g and every group later than g is a proper superset of g, with \emptyset being the trivial first group and G being the trivial final group.
You could still distinguish “fully escalating groupings” from “partially escalating groupings”. Calling a fully escalating grouping a linearisation might be okay, but adding an extra term might not be helpful. (I’m surprised you’d go with “partial linearisation”, when, given it’s a smaller set than a full linearisation, you could call it a minilinearisation)
The new formulation looks like it makes sense, whatever it’s called though!
Having diag() auto chunk feels like cheating 
Shouldn’t compose return \{ \emptyset, s \} \cup \{\forall x \in L^\prime : x \cup s\} ? (Shouldn’t s be specified as topologically valid here as well?)