Jason (jcreed) wrote,

Sketched some notes about the "periodic table" of possibility/lax-like operators that I know of. The two major sad facts are that it (a) (I think) doesn't yet account for either the Pfenning or Awodey-Bauer proof-irrelevance modalities (though it comes soooo cloooose) and (b) it doesn't yet explain the variation in the monadic mechanism with axiomatization of a relation, which I half-wish it did, because that would justify the labels of K, T, 4, S4, and open the door to maybe further choices.

For example, suppose for some reason I wanted a lax-like modal operator that had ◯◯◯A |- ◯◯A but not ◯◯A |- ◯A. If there were a relation I could talk about, I could say "anything accessible in three hops is accessible in two", but there isn't yet, so I can't.
Tags: logic, math, modal

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