For Kant, logical truth arises from the structure of the discursive intellect (i.e., an intellect that relates to objects indirectly, by means of concepts). Discursive cognition necessarily involves application of the categories, so we know a priori that the world as experienced by the discursive knower will consist of objects-with-properties standing in ground-consequent relations. This means that logical truths count as (roughly) analytic in Kant's famous dichotomy of analytic/synthetic, but the analytic truths involved aren't trivially definitional, but deep, contentful truths uncovered by delicate ‘exposition’ that's subject to error and often incomplete. Furthermore, just as the a priori truths of geometry are true only of the world as experienced by discursive cognizers with our spatiotemporal forms of intuition, likewise the a priori truths of logic are true only of the world as experienced by any discursive cognizer whatsoever. Thus logic is also, in a sense, transcendentally ideal.
Keywords: analytic, a priori, categories, discursive intellect, forms of intuition, logical truth, synthetic, transcendental idealism