Kant distinguishes between general logic and transcendental logic. The former (Aristotelian) studies the laws of thought whatever the contents. (many disputes arise from his arbitrary division).
Kant defines transcendental logic, on the other hand, as a subdivision of general logic, and distinguishes it from general logic in so far as transcendental logic does not abstract from all the contents of knowledge, but takes from transcendental aesthetics the forms of pure intuition of space and time into consideration, thus abstracting from empirical contents, whilst still accounting for pure intuitions.
Transcendental logic in Kant’s (no clearer) words is:
‘In the expectation that there may perhaps be conceptions which relate a priori to objects, not as pure or sensuous intuitions, but merely as acts of pure thought (which are therefore conceptions, but neither of empirical nor of aesthetical origin) – in this expectation, I say, we form to ourselves, by anticipation, the idea of a science of pure understanding and rational (Vernunfterkenntniss) cognition, by means of which we may cogitate objects entirely a priori. A science of this kind, which should determine the origin, the extent, and the objective validity of such cognitions, must be called Transcendental Logic, because it has not, like general logic, to do with the laws of understanding and reason in relation to empirical as well as pure rational cognitions without distinction, but concerns itself with these only in an a priori relation to objects.’p.66
Analytic is used in its etymological significance too [as in Aristotle] as what breaks something down to its costitutive elements (from analyo: to melt). Transcendental analytics will break down the essential elements of understanding. In the introduction to the transcendental analytic Kant makes an interesting remark about truth and logic. He asserts that in so far as truth consists in the accordance of a cognition to a given object, there can be no universal criterion for establishing truth and that a ‘sufficient and at the same time universal test of truth cannot possibily be found’. (67) However, such criterion can be established for the form of cognition, even though ‘although cognition may be perfectly accurate as to logical form, that is, not self-contradictory, it is notwithstanding quite possible that it may not stand in agreement with its object.’ Thus logic can only be the negative criterion of truth, insufficient to establishing it, yet necessary to examine the coherence of information gathered around an object. Dialectic is the misapplication of logic whereby the material content of cognition has been subsumed to the formal laws of acquiring information and lost its empirical specificity. Click on the links to follow Kant in his division.