(0,1)-category theory: logic, order theory
proset, partially ordered set (directed set, total order, linear order)
distributive lattice, completely distributive lattice, canonical extension
natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism = propositions as types +programs as proofs +relation type theory/category theory
A modal logic is uniform if it is closed under the rule of uniform substitution of $\mathcal{L}_\omega(n)$-formulae for propositional variables and is normal if it also contains the axiom schemata:
(K) $\Diamond_i(\psi \vee \chi) \to \Diamond_i(\psi)\vee \Diamond_i(\chi)$
(N) $\neg \Diamond_i(\bot)$
and monotonicity (for each $i$):
if $\psi \to \chi \in \Lambda$ then $\Diamond_i \psi \to \Diamond_i \chi \in \Lambda$.
The smallest normal modal logic with $m$ ‘agents’ is K(m). (The diamonds correspond to the $M_i$ of that entry.)