In this article, we define ArgSciFF, a prototype operational argumentation framework to support dialogic argument exchange between Semantic Web services. ArgSciFF is based on the Sciff abductive-logic programming (ALP) framework. (Sciff is an abbreviation for "IFF with constraints for agent societies," referring to the "if and only if' proof procedure developed by Tze Ho Fung and Robert Kowal-ski.) In ArgSciFF, an intelligent agent can interact with a Web service and reason from the interaction result. The reasoning semantics is an argumentation semantics that views the interaction as a dialogue. The dialogue lets two parties exchange arguments and attack, challenge, and justify them on the basis of their knowledge. This format has the potential to overcome a well-known barrier to human users' adoption of IT solutions because it permits interaction that includes justified answers that can be reasoned about and rebutted.