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We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a gener-alisation of Theorist. The generalisation allows any theory formulated in a monotonic logic… (More)

We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures… (More)

In recent years, argumentation has been shown to be an appropriate framework in which logic programming with negation as failure as well as other logics for non-monotonic reasoning can be encompassed. Many of the existing semantics for negation as failure in logic programming can be understood in a uniform way using argumentation. Moreover, other logics for… (More)

We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system. The proof procedures find a set of assumptions, to… (More)

The notion of assumption-based framework generalises and reenes the use of abduction to give a formalisation of non-monotonic reasoning. In this framework, a sentence is a non-monotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumptions. The notion of acceptability for such assumptions is… (More)

was developed, starting in the 90s, as a computational framework to reconcile and generalise most existing approaches to default reasoning [24, 25, 4, 3, 27, 26]. ABA was inspired by Dung's preferred extension semantics for logic programming [10, 7], with its di-alectical interpretation of the acceptability of negation-as-failure assumptions based on the… (More)

Bondarenko et al. have recently proposed an abstract framework for default reasoning. Besides capturing most existing formalisms and proving that their standard semantics all coincide, the framework extends these formalisms by generalising the semantics of admissible and preferred arguments , originally proposed for logic programming only. In this paper we… (More)

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… (More)

A multiagent system may be thought of as an artificial society of autonomous software agents and we can apply concepts borrowed from welfare economics and social choice theory to assess the social welfare of such an agent society. In this paper, we study an abstract negotiation framework where agents can agree on multilateral deals to exchange bundles of… (More)

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for ab-ductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints… (More)