A Mathematical Treatment of Defeasible Reasoning and its Implementation

We present a mathematical approach to defeasible reasoning. This approach is based on the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. We combine the ideas of the two. This main contribution of this paper is a precise well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. We prove that an order relation can be introduced among equivalence classes under the equi-specificity relation. We also prove a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning

A Framework for Combining Defeasible Argumentation with Labeled Deduction

In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common notions (such as the concept of argument, defeater, etc.) along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in which many important issues concerning defeasible argumentation are captured within a unified logical framework. We also discuss some logical properties and extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin

Defeasible Logic Programming: An Argumentative Approach

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, ie, the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.Comment: 43 pages, to appear in the journal "Theory and Practice of Logic Programming

Local logics, non-monotonicity and defeasible argumentation

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of Barwise and Seligman’s logic of information flow.We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of argument systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligman’s representation of commonsense reasoning.Fil: Bodanza, Gustavo Adrian. Universidad Nacional del Sur. Departamento de Humanidades; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Universidad Nacional del Sur. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin