Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation
This provides a foundational framework for reasoning about discussion and argumentation in AI, addressing a gap in formal methods for handling diverse models.
The paper tackles the lack of a formal reasoning framework for diverse discussion and argumentation models in AI by formulating a discussion-graph semantics for first-order logic with equality, and it shows that generalised extensions and acceptability semantics are first-order characterisable, with propositional characterisability as an immediate consequence.
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a formal reasoning framework capable of handling diverse discussion and argumentation models. Second, we generalise Dung's notion of extensions to cases where two or more graph nodes in an argumentation framework are equivalent. Third, we connect these two contributions by showing that the generalised extensions are first-order characterisable within the proposed discussion-graph semantics. Propositional characterisability of all Dung's extensions is an immediate consequence. We furthermore show that the set of all generalised extensions (acceptability semantics), too, are first-order characterisable. Propositional characterisability of all Dung's acceptability semantics is an immediate consequence.