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
basic constructions:
strong axioms
As a category has internal logic, so a (∞,1)-category has internal $(\infty,1)$-logic
See
(∞,1)-type theory, (∞,1)-logic