Abstract. In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules. We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the “admissibility ” semantics for all these formalisms has a natural argumentationtheoretic interpretation and proof procedure, which seem to correspond well with informal argumentation. In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its non-provability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of non-provability claims. 1.

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Although reasoning about what is the case has been the historic focus of logic, reasoning about what should be done is an equally important capacity for an intelligent agent. Reasoning about what to do in a given situation- termed practical reasoning in the philosophical literature- has important differences from reasoning about what is the case. The acceptability of an argument for an action turns not only on what is true in the situation, but also on the values and aspirations of the agent to whom the argument is directed. There are three distinctive features of practical reasoning: first, that practical reasoning is situated in a context, directed towards a particular agent at a particular time; second, that since agents differ in their aspirations there is no right answer for all agents, and rational disagreement is always possible; third, that since no agent can specify the relative priority of its aspirations outside of a particular context, such prioritisation must be a product of practical reasoning and cannot be used as an input to it. In this paper we present a framework for practical reasoning which accommodates these three distinctive features.

One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as NP, co-NP, and  ¢¡ £. In consequence, a number of researchers have considered methods for specialising the structure of such systems so as to identify classes for which efficient decision processes exist. In this paper the effect of a number of graph-theoretic restrictions is considered: ¤-partite systems (¤¦¥¨ § ) in which the set of arguments may be partitioned into ¤ sets each of which is conflict-free; systems in which the numbers of attacks originating from and made upon any argument are bounded; planar systems; and, finally, those of ¤-bounded treewidth. For the class of bipartite graphs, it is shown that determining the acceptability status of a specific argument can be accomplished in polynomial-time under both credulous and sceptical semantics. In addition we establish the existence of polynomial time methods for systems having bounded treewidth when deciding the following: whether a given (set of) arguments is credulously accepted; if the system has a non-empty preferred extension; has a stable extension; is coherent;

Abstract. In this paper, we present a decision support system which is built upon an argumentation framework for practical reasoning. A logic language is used as a concrete data structure for holding statements representing knowledge, goals, and decisions. Different priorities are attached to these items, corresponding to the probability of the knowledge, the preferences between goals, and the expected utilities of decisions. These concrete data structures consist of information providing the backbone of arguments. Due to the abductive nature of practical reasoning, arguments are built by reasoning backwards, and possibly by making suppositions over missing information. Moreover, arguments are defined as tree-like structures. In this way, our computer system, implemented in Prolog, suggests some solutions and provides an interactive and intelligible explanation of this choice. 1

Abstract. In this paper, we present a model of agents which use argumentation to select and compose services in open and distributed environments. For this purpose, we propose a modular agent architecture using three main modules, dedicated, respectively, to decision making, communication, and negotiation. We deploy a simple “virtual ” travel agent example to illustrate how our agents select and compose services, focusing on the functionalities of the modules within the agents. 1

Abstract. We present the CaSAPI system, implementing (a generalisation of) three existing computational mechanisms [8–10] for determining argumentatively whether potential beliefs can be deemed to be acceptable and, if so, for computing supports for them. These mechanisms are defined in terms of dialectical disputes amongst two fictional agents: a proponent agent, eager to determine the acceptability of the beliefs, and an opponent agent, trying to undermine the existence of an acceptable support for the beliefs, by finding attacks against it that the proponent needs to counter-attack in turn. The three mechanisms differ in the level of scepticism of the proponent agent and are defined for (flat) assumption-based argumentation frameworks [3]. Thus, they can serve as decision-making mechanisms for all instances of these frameworks. In this paper we show how they can be used for logic programming, legal reasoning, practical reasoning, and agent reasoning. 1

The majority of existing work on agent dialogues considers negotiation, persuasion or deliberation dialogues; we focus on inquiry dialogues, which allow agents to collaborate in order to find new knowledge. We present a general framework for representing dialogues and give the details necessary to generate two subtypes of inquiry dialogue that we define: argument inquiry dialogues allow two agents to share knowledge to jointly construct arguments; warrant inquiry dialogues allow two agents to share knowledge to jointly construct dialectical trees (essentially a tree with an argument at each node in which a child node is a counter argument to its parent). Existing inquiry dialogue systems only model dialogues, meaning they provide a protocol which dictates what the possible legal next moves are but not which of these moves to make. Our system not only includes a dialogue-game style protocol for each subtype of inquiry dialogue that we present, but also a strategy that selects exactly one of the legal moves to make. We propose a benchmark against which we compare our dialogues, being the arguments that can be constructed from the union of the agents ’ beliefs, and use this to define soundness and completeness properties that we show hold for all inquiry dialogues generated by our system.

Abstract There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logicbased argumentation is that an argument is a pair 〈Φ, α 〉 where Φ is minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation. Classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue. Here we propose ameliorating this problem by using connection graphs to give information on the ways that formulae of the knowledgebase can be used to minimally and consistently entail a claim. Using a connection graph allows for a substantially reduced search space to be used when seeking all the arguments for a claim from a knowledgebase. We provide a theoretical framework and algorithms for this proposal, together with some theoretical results and some preliminary experimental results to indicate the potential of the approach. 1

Legal doctrines provide principles, guidelines and rules for dispute resolution in reasoning with cases. To apply legal doctrines, the context of a contract consisting of different knowledge bases about beliefs and expertise of contract parties as well as about common social, legal domains need to be established. Judges then decide legal outcomes by reasoning from factors drawn in contract contexts following legal doctrines. In this paper, we model this decision making by modular argumentation. We focus on legal doctrines in contract law, especially the doctrines of impossibility and frustration of purpose.