An example of Dialectical-Algorithmic could be the issue of Socionics and MBTI(and other MBTTian systems). If you're from the Socionics camp, then you pretty much agree MBTI has a faulty system, but still holds validity in terms of the types and general basics of functional typology. All MBTTian systems - that is, those that derive themselves from the Myers-Briggs interpretation of Jungian theory(Pod'Lair, Keirsey, JCF) are all essentially the same thing as MBTI, because they work on Je = J ; Pe = P.
So you have a dilemma of Augusta's interpretation and Socionics versus the Myers-Briggs interpretation and MBTT. An expert Socionist is more likely the one to realize that, although MBTT is faulty and inaccurate, and Socionics is the more accurate, consistent and applicable theory, still there is the actual phenomenon out there which cannot be systematized so precisely. Also, in the early stages of conflict, a dialectical-algorithmic thinker would seek to find a link between MBTI and Socionics, to see if they are both valid(here is my own attempt to find a link), but if they are not, then argue dialectically why one of them has to be invalid(in this case, MBTI, and it's function flips for Introverts, which are the cause of the controversy; this is what invalidates MBTI, it's heavily inconsistent on a functional level). This entails heavy perspective tweaking, as that is pretty much all it is. A dissonance of perspectives.
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