Classical logic, argument and dialectic

A well studied instantiation of Dung's abstract theory of argumentation yields argumentation-based characterisations of non-monotonic inference over possibly inconsistent sets of classical formulae. This provides for single-agent reasoning in terms of argument and counter-argument, and distributed non-monotonic reasoning in the form of dialogues between computational and/or human agents. However, features of existing formalisations of classical logic argumentation (Cl-Arg) that ensure satisfaction of rationality postulates, preclude applications of Cl-Arg that account for real-world dialectical uses of arguments by resource-bounded agents. This paper formalises dialectical classical logic argumentation that both satisfies these practical desiderata and is provably rational. In contrast to standard approaches to Cl-Arg we: 1) draw an epistemic distinction between an argument's premises accepted as true, and those assumed true for the sake of argument, so formalising the dialectical move whereby arguments\u2019 premises are shown to be inconsistent, and avoiding the foreign commitment problem that arises in dialogical applications; 2) provide an account of Cl-Arg suitable for real-world use by eschewing the need to check that an argument's premises are subset minimal and consistent, and identifying a minimal set of assumptions as to the arguments that must be constructed from a set of formulae in order to ensure that the outcome of evaluation is rational. We then illustrate our approach with a natural deduction proof theory for propositional classical logic that allows measurement of the \u2018depth\u2019 of an argument, such that the construction of depth-bounded arguments is a tractable problem, and each increase in depth naturally equates with an increase in the inferential capabilities of real-world agents. We also provide a resource-bounded argumentative characterisation of non-monotonic inference as defined by Brewka's Preferred Subtheories

An Argumentation Based Semantics for Agent Reasoning.

Abstract. A key challenge for agent architectures and programming paradigms is to account for defeasible reasoning over mental attitudes and to provide as-sociated conflict resolution mechanisms. A growing body of work is looking to address these challenges by proposing argumentation based approaches to agent defeasible and practical reasoning. This work conforms to Dung’s seminal ar-gumentation semantics. In this paper we review our previous work in which we extend Dung’s semantics to allow for inclusion of arguments that express pref-erences between other arguments. In this way we account for the fact that pref-erence information required to resolve conflicts is itself defeasible and may be conflicting. We then propose the extended semantics as a semantics for agent defeasible and practical reasoning, and substantiate this claim by showing how our semantics can characterise, and indeed provide a framework for extending, existing approaches to agent reasoning over beliefs, goals, and actions.