Tonight I reformulated my definitions, again!
But the revision is only regarding my causal theory. Lucky I’m doing this right before I publish it.
Now:
“A system-set is a family over $\supseteq_{\top} - \{<\top, \bot>\}$; its elements called systems.”
(it’s better when a system is transitive that we say it “narrows” assignment set s to assignment set s’ …)
Then here immediately comes my elegant definition pair for “determination and contribution”, which together with the “injective” condition covered by transitive closures lays the path for the rest of my definitions:
“A system is causal iff …”
“A system is informational iff it is causal and …”
Then I use “saturated causal system sets” as models for the recursive truth-condition definitions to establish the semantics.
Now the whole thing is even more beautiful.
