What is the Importance of Logic in Buddhist soteriology?

Many scholastic systems of Buddhist thought seem to have develop highly sophisticated systems of epistemology and logic (e.g., pramāṇa theory in the works of Dignāga and Dharmakīrti), as well as dialectical reasoning in Madhyamaka (e.g., Nāgārjuna).The question which arises here is Can inferential cognition and logic ever give rise to liberating wisdom, or is liberation strictly dependent on non-conceptual perception? If ultimate truth is said to be beyond conceptual elaboration, how can logically mediated analysis contribute to its realization without remaining confined to the conventional level?