Towards a Logic-Based Theory of Argumentation

There are a number of frameworks for modelling argumentation in logic. They incorporate formal representation of individual arguments and techniques for comparing conflicting arguments. In these frameworks, if there are a number of arguments for and against a particular conclusion, an aggregation function determines whether the conclusion is taken to hold. We propose a generalization of these frameworks. In particular, this new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against(in most other frameworks, aggregation functions just consider the existence of arguments for and against). In this paper, we explore this framework (based on classical logic) in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula). Introduction Modelling argumentation has been a subject of research as long as the study of logic. They are closely intertwined topics, and modelling argumentation in logic is a natural, and important, research goal. A useful introduction to argumentation is in (Tou58), and a comprehensive recent review of modelling argumentation in logics is in (PV00). Since paraconsistent logics have been suggested for applications including reasoning with specifications (HN98) and reasoning with news reports in structured text (Hun00), a logic-based theory of argumentation such as proposed below may be applicable in various roles. Whilst most proposals have been made for modelling argumentation in logic, all are limited in the way that they combine arguments for and against a particular conclusion following. None are sensitive to the number of arguments for and against, apart from some proposals for counting the number for and the number against, and if there are more arguments for, then the conclusions follows, otherwise it is defeated. Most proposals for modelling argumentation in logic are based on some form of binary argumentation (only the existence of arguments for and against is considered). A simple Copyright c 2000, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. form of argumentation is that a conclusion follows if and if only if there is an argument for the conclusion, and no argument against the conclusion. So a conclusion follows only if it is not rebutted. A development of this idea is to only consider arguments that have not been undercut, and to check this by recursion for subarguments. An argument is undercut if and only if one of the assumptions for the argument is rebutted. Each undercut to a subargument is itself an argument and so may be undercut, and so by recursion each undercutter needs to be considered. In this paper, we propose a new framework for argumentation with non-binary aggregation functions. For this framework, we have the following requirements: to derive arguments from a set of formulae that is potentially inconsistent; to compare arguments for and against a particular consequent; to identify undercuts for each argument, and by recursion, to identify undercuts for all subarguments for an argument; to evaluate each argument in terms of all its undercuts, and by recursion, all undercuts to its subarguments, and the value assigned to an argument decreases with increasing number of undercuts, and increases with increasing number of undercuts to each of the undercuts of the subarguments; to accumulate arguments for a consequent so that each extra argument contributes less to the accumulated value; In our framework, that is based on classical logic, an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula). Non-binary aggregation functions can be defined that are sensitive to the number of arguments for and against a conclusion. This paper defines the framework and explores its properties.