A computational framework is presented for the generation of elementary speech acts to establish conceptual alignment between a computer system and its user. This article clearly distinguishes between 2 phases of the alignment process: message interpretation and message generation. In the interpretation phase, presuppositions are extracted from the user's message and compared with the system's semantic model of the application domain, which is represented in Type Theory. Subsequently, in the generation phase, a feedback message at the conceptual level is produced to resolve detected discrepancies and avoid potential discrepancies as a result of quantity implicatures. A conversational strategy is provided that is based on Gricean maxims and a differentiation of various types of information states of the system, such as private and common beliefs about the domain of discourse. (Contains 7 footnotes, 2 figures, and 4 tables.)