Argument Theory Change Applied to Defeasible Logic Programming

In this article we work on certain aspects of the belief change theory in order to make them suitable for argumentation systems. This approach is based on Defeasible Logic Programming as the argumentation formalism from which we ground the definitions. The objective of our proposal is to define an argument revision operator that inserts a new argument into a defeasible logic program in such a way that this argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the defeasible logic program has to be changed in concordance with a minimal change principle. Finally, we present an algorithm that implements the argument revision operation. Introduction & Motivation This work presents a first approach to introduce several concepts of belief revision within the area of argumentation systems. We are particularly focused on the revision of a knowledge base by an argument. To achieve this, we use Defeasible Logic Programming (DELP) (Garcı́a and Simari 2004) as the knowledge representation language, thus, knowledge bases will be represented as defeasible logic programs (DELP-programs). The DELP formalism is briefly described in the next section. The main objective is to define an argument revision operator that ensures warrant of the conclusion of the (external) argument being added to a defeasible logic program. When we revise a program by an argument 〈A, α〉 (where A is an argument for α), the program resulting from the revision will be such that A is an undefeated argument and α is therefore warranted. In that sense, this operator will be prioritized. Thus, we refer to this operator as warrant-prioritized argument revision operator (WPA Revision Operator). The main issue underlying warrant-prioritized argument revision (addressed in the third section of this paper) lies in the selection of arguments and the incisions that have to be made over them. An argument selection criterion will determine which arguments should not be present in order to ensure the inserted argument is undefeated. Once this selection Copyright c © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. This work is partially supported by CONICET (PIP 5050), Universidad Nacional del Sur and ANPCyT. is made, incisions (in the form of deletion of rules) will make those arguments “disappear”; but this process has to be done carefully, following some minimal change principle. In the fourth section, we present two examples of minimal change, thus defining the way the warrant-prioritized revision operator behaves. A general algorithm for argument revision is proposed in the closing part of this section. Finally, in the last section, related work is discussed, future work is proposed, and conclusions are drawn. Elements of Defeasible Logic Programming Defeasible Logic Programming (DELP) combines results of Logic Programming and Defeasible Argumentation. The system is fully implemented and is available online (LIDIA 2007), and a brief explanation of its theory is included below. A DELP-program P is a set of facts, strict rules and defeasible rules. Facts are ground literals representing atomic information or the negation of atomic information using strong negation “∼”. Strict Rules represent non-defeasible information noted as α← β1, . . . , βn, where α is a ground literal and βi>0 is a set of ground literals. Defeasible Rules represent tentative information noted as α –≺β1, . . . , βn, where α is a ground literal and βi>0 is a set of ground literals. When required, P will be denoted (Π,Δ) distinguishing the subset Π of facts and strict rules, and the subset Δ of defeasible rules (see Ex. 1). From a program (Π,Δ), contradictory literals could be derived. Nevertheless, the set Π (which is used to represent non-defeasible information) must possess certain internal coherence, that is, no pair of contradictory literals can be derived from Π. Strong negation can be used in the head of a rule, as well as in any literal in its body. In DELP, literals can be derived from rules as in logic programming, being a defeasible derivation one that uses, at least, one defeasible rule. Example 1 Consider the DELP-program P1 = (Π1,Δ1): Π1= { t, z, (p← t) } Δ1= { (∼a –≺y), (y –≺x), (x –≺z), (y –≺p), (a –≺w), (w –≺y), (∼w –≺t), (∼x –≺t), (x –≺p) } From a program is possible to derive contradictory literals, e.g., from (Π1,Δ1) of Ex. 1 it is possible to derive a and ∼a. DELP incorporates a defeasible argumentation formalism for the treatment of contradictory knowledge. This Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence (2008)