We study defeasible knowledge bases with conditional preferences (DKB). A DKB consists of a set of undisputed facts and a rule-based system that contains different types of rules: strict, defeasible, and preference. A major challenge in defining the semantics of DKB lies in determining how conditional preferences interact with the attack relations represented by rebuts and undercuts, between arguments. We introduce the notions of preference attack relations as sets of attacks between preference arguments and the rebuts or undercuts among arguments as well as of preference attack relation assignments which map knowledge bases to preference attack relations. We present five rational properties (referred to as regular properties), the inconsistency-resolving, effective rebuts, context-independence, attack monotonicity and link-orientation properties generalizing the properties of the same names for the case of unconditional preferences. Preference attack relation assignment are defined as regular if they satisfy all regular properties. We show that the set of regular assignments forms a complete lower semilattice whose least element is referred to as the canonical preference attack relation assignment. Canonical attack relation assignment represents the semantics of preferences in defeasible knowledge bases as intuitively, it could be viewed as being uniquely identified by the regular properties together with the principle of minimal removal of undesired attacks. We also present the normal preference attack relation assignment as an approximation of the canonical attack relation assignment.

Properties like logical closure and consistency are important properties in any logical reasoning system. Caminada and Amgoud showed that not every logic-based argument system satisfies these relevant properties. But under conditions like closure under contraposition or transposition of the monotonic part of the underlying logic, ASPIC-like systems satisfy these properties. In contrast, the logical closure and consistency properties are not well-understood for other well-known and widely applied systems like logic programming or assumption based argumentation. Though conditions like closure under contraposition or transposition seem intuitive in ASPIC-like systems, they rule out many sensible ASPIC-like systems that satisfy both properties of closure and consistency. We present a new condition referred to as the self-contradiction axiom that guarantees the consistency property in both ASPIC-like and assumption-based systems and is implied by both properties of closure under contraposition or transposition. We develop a logic-associated abstract argumentation framework, by associating abstract argumentation with abstract logics to represent the conclusions of arguments. We show that logic-associated abstract argumentation frameworks capture ASPIC-like systems (without preferences) and assumption-based argumentation. We present two simple and natural properties of compactness and cohesion in logic-associated abstract argumentation frameworks and show that they capture the logical closure and consistency properties. We demonstrate that in both assumption-based argumentation and ASPIC-like systems, cohesion follows naturally from the self-contradiction axiom. We further give a translation from ASPIC-like systems (without preferences) into equivalent assumption-based systems that keeps the self-contradiction axiom invariant.

Two well-known but distinct approaches to reasoning with inconsistent knowledge bases are structured argumentation and preferred subtheories. Recently, it has been showed that stratified preferred subtheories, an important class of preferred subtheories, could be represented naturally in structured argumentation though it remains open whether general preferred subtheories could be captured in the later as well? Structured argumentation could be viewed as an integration of preference-dependent argumentation employing preference-dependent attacks and preference-independent argumentation embodied by assumption-based argumentation. In this article, we show that preferred subtheories could be transformed in a simple way into assumption-based argumentation. We also give counter examples to show that the natural translation of stratified preferred subtheories into preference-dependent argumentation proposed in the literature does not capture the semantics of general preferred subtheories.

We propose an argument-based foundation for dialogue games capable of modelling protocols for exchange of arguments in dialogues to prove or disprove propositions. We introduce structure into dialogue states by modelling them as dialogue trees coupled with appropriate annotation mechanisms. We model dialogue locutions as transformations between dialogue states. Viewing dialogues as proofs, we study conditions for them to be sound under the grounded semantics and the credulous semantics in argumentation. Thank to annotation mechanisms, we could handle backtracking of proponent in dialogue games.

An abstract argumentation framework may have many extensions. Which extension should be adopted as the semantics depends on the sceptical attitudes of the reasoners. Different degrees of scepticism lead to different semantics ranging from the grounded extension as the most sceptical semantics to preferred extensions as the least sceptical semantics. Extending abstract argumentation to allow attacks to be attacked, subjects attacks to argumentation and hence gives rise to a new dimension of scepticism for characterizing how sceptically attacks are accepted. In this article, we present a semantics based on the notion of inductive (grounded) defense of attacks which is sceptical towards the acceptance of attacks but credulous towards the acceptance of arguments.We show that the semantics preserves fundamental properties of abstract argumentation including the monotonicity of the characteristic function. We further show that any extension of the semantics proposed by Gabbay; Baroni, Cerutti, Giacomin and Guida; and Modgil contains a sceptical part being an extension of our semantics, and a credulous part resulted from its credulousness towards the acceptance of attacks. We then introduce a stratified form of extended argumentation which still allows an unbounded number of levels of attacks against attacks while assuring that all proposed semantics coincide. In this article, we also develop a sound and complete dialectical proof procedure for the presented semantics following a model of dispute that alternates between argumentation to accept arguments and to accept attacks.

We propose an argumentation framework for modelling jury-based dispute resolution where the dispute parties present their arguments before a judge and a jury. While the judge as the arbiter of law determines the legal permissibility of the presented arguments the jurors as triers of facts determine their probable weights. Such a framework is based on two key components: classical argumentation frameworks containing legally permissible arguments and probabilistic spaces assigning probable weights to arguments. A juror's probability space is represented by a set of possible worlds coupled with a probabilistic measure computed by assumption-based argumentation framework using grounded semantics.

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.

We present a common framework for dialectical proof procedures for computing credulous, grounded, ideal and sceptical preferred semantics of abstract argumentation. The framework is based on the notions of dispute derivation and base derivation. Dispute derivation is a dialectical notion first introduced for computing credulous semantics in assumption-based argumentation, and adapted here for computing credulous semantics and grounded semantics. Base derivation is introduced for two purposes: (i) to characterize all preferred extensions containing a given argument, and (ii) to represent backtracking in the search for a dispute derivation. We prove the soundness of the proof procedures for any argumentation frameworks and their completeness for general classes of finitary or finite-branching argumentation frameworks containing the class of finite argumentation frameworks as a subclass.We also discuss related results.

An information agent is viewed as a deductive database consisting of three parts: an observation database containing the facts the agent has observed or sensed from its surrounding environment; an input database containing the information the agent has obtained from other agents; an intensional database which is a set of rules for computing derived information from the information stored in the observation and input databases. Stabilization of a system of information agents represents a capability of the agents to eventually get correct information about their surrounding despite unpredictable environment changes and the incapability of many agents to sense such changes causing them to have temporary incorrect information. We argue that the stabilization of a system of cooperative information agents could be understood as the convergence of the behavior of the whole system toward the behavior of a “superagent”, who has the sensing and computing capabilities of all agents combined. We show that unfortunately, stabilization is not guaranteed in general, even if the agents are fully cooperative and do not hide any information from each other. We give sufficient conditions for stabilization. We discuss the consequences of our results.