Here’s a really rough thumbnail sketch of a non-question begging argument refuting Fristianity (written from my phone).
In Christianity, the categorical three term syllogism (“Barbara”) is grounded in the intratrinitarian relationships within the Godhead:
1.) All that belongs to the Son (B) belongs to the Father (A).
2.) All that belongs to the Spirit (C) belongs to the Son (B).
3.) Therefore, all that belongs to the Spirit (C) belongs to the Father (A).
1.) All Bs are As.
2.) All Cs are Bs.
3.) Therefore, all Cs are As.
The Fristian quadrinity, even with a mysterious role for the fourth person, by the nature of the unity in the quadrinity would produce a four term syllogism, which is formally fallacious. The Fristian god cannot provide the necessary preconditions for logic.
(Argument inspired by Vern Poythress.)