As an example: I've related Alpha Ti to resolving contradictions (one of the few areas where Model A2 and Model G overlap in their semantics), but there are different ways to resolve contradictions.
The source of all conflict is contradiction: two different parties may have different beliefs or values that cause them to want different outcomes or states: one wants P to be true and one wants ~P (not-P) to be true. The most obvious way to resolve a conflict is simply for one party to win and make P true (or ~P). This is most like a Beta strategy: bSe can be used to dominate the other party outright and ensure the desired outcome, and bFe can be used to convince him, so that he wants the same thing you do.
Symbolically we can represent this as
P & ~P → P (or ~P)
(with the arrow representing a state transition, not logical implication)
The issue with the Beta approach is, how do you choose which one it is and make sure that it's right? Alpha Ti(Ne) on the other hand resolves the conflict by finding a context (model, interpretation, etc.) in which one is true and another in which the other is true. Symbolically:
P & ~P → (A ⊨ P) & (B ⊨ ~P)
This avoids arbitrarily choosing one, and allows joining the two together in some kind of more comprehensive understanding. Socially, this means creating an environment where people can interact and coexist peacefully, FeSi. The issue with the Alpha approach is that it's not always clear what information to add to make each one true (and of course one might just be false).
Delta FiNe is similar to TiNe, except that we associate an individual to each proposition instead:
P & ~P → P(x) & ~P(y)
Propositions are associated with Ti and individuals with Fi, so the move from propositional logic to predicate logic is like adding Fi to Ti. An individual is not so different from a context or model except that it's "inside" the proposition attributed to it, while the model is "outside". Both give a way of adding hidden contextual information.
Socially, this means that Delta prefers to allow each individual to have their own view and non-interfering sphere of influence. (Clearly this is not possible in many situations, and tends to result in conflict-avoidance or acquiescence in practice.)
For Gamma we can say that as the opposite of Alpha it does not seek to resolve the contradiction or conflict in the first place. It shares acceptance of conflict with Beta and individual differences with Delta. So each quadra is a preferred method of conflict resolution, and Gamma may use the Beta or Delta methods as needed — most typically Gammas don't try to get everyone to agree internally on their values and beliefs, but will still engage in conflict if a particular desire is being obstructed. Arguably the Gamma approach can be short-sighted in that different values almost inevitably lead to conflict later on. Maybe there is a refinement of logic that can express the Gamma approach more easily, to distinguish between internal and external state.
Augusta tried to interpret conflict in terms of information, attributing it to different areas of interest and miscommunication. But in practice, conflict is due to very real differences in how we want the world to be — information metabolism includes both input and output, perception and manipulation of information and state.
