Consequence Operators for Defeasible Argumentation: characterization and logical properties ? Carlos Iv¶an Ches~nevar, cic@cs.uns.edu.ar Guillermo Ricardo Simari, grs@cs.uns.edu.ar Departamento de Ciencias de la Computaci¶ on { Universidad Nacional del Sur Av.Alem 1253 { B8000CPB Bah¶³a Blanca { Rep¶ ublica Argentina Tel/Fax: (+54) (291) 459 5135/5136 { Email: fcic,grsg@cs.uns.edu.ar Abstract. Arti¯cial Intelligence (AI) has long dealt with the issue of ¯nding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con°uence point for many alternative logical frameworks. Di®erent formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other con°icting arguments. In this context, defeasible consequence relationships for modeling argument and warrant as well as their logical properties have gained particular attention. This paper discusses two consequence operators for the LDS ar framework for defeasible argumentation. The operators are intended for modeling argument construction and dialectical analysis (warrant), re- spectively. Their associated logical properties are studied and contrasted with SLD-based Horn logic. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. Key words: defeasible argumentation; knowledge representation; non-monotonic inference; labeled deduction. 1 Introduction and motivations Arti¯cial Intelligence (AI) has long dealt with the issue of ¯nding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con°uence point for many alternative logical frameworks. Di®erent formalisms have been developed, most of them sharing the common notions of ar- gument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other con°icting arguments. In this context, defeasible consequence relationships for modeling argument and warrant as well as their logical properties have gained particular attention. The study of logical properties of defeasible argumentation motivated the development of LDS ar [Che01], an argumentation formalism based on the labeled deduction methodol- ogy [Gab96]. In labeled deduction, the usual notion of formula is replaced by the notion of labeled formula, expressed as Label :f, where Label represents a label associated with the w® f. A labeling language L Label and knowledge-representation language L kr can be combined to provide an enriched object language, in which labels convey additional information also encoded at object-language level. This paper introduces two consequence operators C arg and C war , used for argument con- struction and warrant computation, respectively. These operators were de¯ned within the ? The paper summarizes some of the main results of the ¯rst author's PhD Thesis [Che01] written under the direction of Guillermo Simari. An electronic version of the Thesis is available at http:nncs.uns.edu.arn»cic