how I think of logic

[gusl]

from a comment I left at jcreed's:

I really like this logic stuff. It's nice math. Especially when you have nice semantics, especially if you have more than one and can shift perspective between the different interpretations.

I think of ordinary logics as being restricted fragments of "universal logic" (i.e. something like lambda calculus). And from there down, we have the classical tradeoff between expressibility and decidability. Different kinds of restriction can deliver different kinds of nice properties, e.g. decidability, completeness, time bounds on decision problems / proof finding, etc.

Anyway, it's fun to come up with translations, interpretations, etc, that link the different ways of expressing things.

I would probably do lots of logic if I didn't hate the work of reading math papers / textbooks (in their current static form).