This chapter introduces a novel computational framework for analyzing and supporting invention dialogues, focusing on the interplay between problem-solving and creative reasoning. We propose a formalism for invention dialogues that captures the structure, patterns, and phase transitions. We leverage category-theoretic representation to describe the transformations in idea development, effectively modeling the processes of abstraction, refinement, and integration. Also, we frame invention as a Constraint Satisfaction Problem (CSP), enabling the representation of constraints and dependencies within the design process. Also, we present a Unified Model for Creative Reasoning, integrating dialogue formalism, category theory, and CSP frameworks into a cohesive computational approach. Finally, we explore the pedagogical value of invention dialogues, demonstrating their potential for training and enhancing creative problem-solving skills. Our contributions provide a robust theoretical foundation and practical tools for understanding and fostering innovation in both human and machine contexts in the form of invention dialogues. We evaluate the pedagogical value of automatically constructed invention dialogue and observe a substantial improvement of learning efficiency in comparison to plain text form of learning material.