There is currently a strong trend in developing various design assistant chatbots, but there is limited understanding of how an ideal chatbot should interact to effectively assist designers in conceptual design. This study models and analyzes conflict resolution in the axiomatic theory of design modeling to identify the necessary thinking styles required in the design conflict resolution process. By identifying the required thinking styles in conflict resolution, researchers can gain insight into how design chatbots can assist designers in acquiring these thinking styles during the conflict resolution process.