Argumentation framework

Abstract: 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 ${\mathcal A}$ for $q$ that is warranted, i.e. the argument ${\mathcal A}$ 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.

Abstract: In many cases of disagreement, particularly in situations involving practical reasoning, it is impossible to demonstrate conclusively that either party is wrong. The role of argument in such cases is to persuade rather than to prove, demonstrate or refute. Following Perelman, we argue that persuasion in such cases relies on a recognition that the strength of an argument depends on the social values that it advances, and that whether the attack of one argument on another succeeds depends on the comparative strength of the values advanced by the arguments concerned. To model this we extend the standard notion of Argumentation Frameworks (AFs) to Value-based Argumentation Frameworks (VAFs). After defining VAFs we explore their properties, and show how they can provide a rational basis for the acceptance or rejection of arguments, even where this would appear to be a matter of choice in a standard AF .I n particular we show that in a VAF certain arguments can be shown to be acceptable however the relative strengths of the values involved are assessed. This means that disputants can concur on the acceptance of arguments, even when they differ as to which values are more important, and hence that we can identify points for which persuasion should be possible. We illustrate the above using an example moral debate. We then show how factual considerations can be admitted to our framework and discuss the possibility of persuasion in the face of uncertainty and disagreement as to values.

Abstract: Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logic-programming language with both weak and strong negation, conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled. The semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks.