We propose a new approach for modeling and reconciling conflicting data cleaning actions. Such conflicts arise naturally in collaborative data curation settings where multiple experts work independently and then aim to put their efforts together to improve and accelerate data cleaning. The key idea of our approach is to model conflicting updates as a formal \emph{argumentation framework}(AF). Such argumentation frameworks can be automatically analyzed and solved by translating them to a logic program $P_{AF}$ whose declarative semantics yield a transparent solution with many desirable properties, e.g., uncontroversial updates are accepted, unjustified ones are rejected, and the remaining ambiguities are exposed and presented to users for further analysis. After motivating the problem, we introduce our approach and illustrate it with a detailed running example introducing both well-founded and stable semantics to help understand the AF solutions. We have begun to develop open source tools and Jupyter notebooks that demonstrate the practicality of our approach. In future work we plan to develop a toolkit for conflict resolution that can be used in conjunction with OpenRefine, a popular interactive data cleaning tool.