Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation

Abstract

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.

Typos have been corrected. 1. Definition 14: there were two formulas given to 1 \leq k case. One was longer than the other. The longer one has been deleted. 2. Definition 20: corrected a wrong (..) scope in the last conjunct. 3. Theorem 6: the formula after "iff*" contained t_1, ..., t_k, ...., .... They have been corrected. c_1, ..., c_t, ..., 4. Corollary 2: a minor typo corrected