"force itself on" is a correct and usable phrase in written English.
It is usually used in a figurative sense to describe an action that is difficult or unpleasant and is being forced upon someone or something, either literally or metaphorically. For example, "The relentless heat of summer seemed to force itself on the city, making it hard to escape the oppressive heat."
The significance of this is that if one started not with the class of ∧-boolean valuations (or any other kind of valuational semantics), but with the rules (∧I) and (∧E) themselves, then that class of valuations would force itself on one's attention anyway as the only class of valuations, preservation of truth on each of which coincided with derivability using those rules.
One way or another, change will force itself on the country.
King has a neat theory about how an adapter's voice can force itself on a story.
Does the rigorously formal discourse of the new logicians in some sense force itself on the intellectuals of this period?
But that is futurology, not news, so it is not going to force itself on any front page anytime soon".
If a democratically elected Ukraine chooses not to join NATO -- and Ukrainians are divided on the question -- NATO will not force itself on Ukraine.
The question forces itself on one, whether even this procedure would prevent the extension of the lesion by contiguity to the articular surfaces.
Timasagoras apparently argued that anger was always and entirely bad, and that it forced itself on its victims as a kind of necessity which one was powerless to fight or to treat in others.
To me, history comes off as one big, long, sad tale of Group X forcing itself on Group Y with Group Y trying, successfully or not, to fend off the aggressors.
Precisely this question had forced itself on another writer who consulted me, ten years earlier.
The plot is bare, the dialogue clinically so – underlining the solipsism that has forced itself on our misfit heroine.
