Francesca Toni

An abstract, argumentation-theoretic approach to default reasoning

Abstract 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 generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or “attacked”) if its “contrary” can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic programming. We regard a set of assumptions, in general, as admissible if and only if it is conflict-free and defends itself (by attacking) every set of assumptions which attacks it. We identify conditions for the existence of extensions and for the equivalence of different semantics.

Computing ideal sceptical argumentation

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 for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] that is sound for the sceptical grounded semantics.

Dialectic proof procedures for assumption-based, admissible argumentation

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 defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter-attack all attacks.The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.

Abstract argumentation

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 argumentation-theoretic 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.

Assumption-Based Argumentation

Assumption-Based Argumentation (ABA) [4, 3, 27, 9, 12, 20, 22] 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 dialectical interpretation of the acceptability of negation-as-failure assumptions based on the notion of “no-evidence-to-the-contrary” [10, 7], by the Kakas, Kowalski and Toni interpretation of the preferred extension semantics in argumentation-theoretic terms [24, 25], and by Dung’s abstract argumentation (AA) [6, 8]. Because ABA is an instance of AA, all semantic notions for determining the “acceptability” of arguments in AA also apply to arguments in ABA. Moreover, like AA, ABA is a general-purpose argumentation framework that can be instantiated to support various applications and specialised frameworks, including: most default reasoning frameworks [4, 3, 27, 26] and problems in legal reasoning [27, 13], game-theory [8], practical reasoning and decision-theory [33, 29, 15, 28, 14]. However, whereas in AA arguments and attacks between arguments are abstract and primitive, in ABA arguments are deductions (using inference rules in an underlying logic) supported by assumptions. An attack by one argument against another is a deduction by the first argument of the contrary of an assumption supporting the second argument. Differently from a number of existing approaches to non-abstract argumentation (e.g. argumentation based on classical logic [2] and DeLP [23]) ABA does not have explicit rebuttals and does not impose the restriction that arguments have consistent and minimal supports. However, to a large extent, rebuttals can be obtained “for

Negotiating socially optimal allocations of resources

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 indivisible resources. We then analyse how these deals affect social welfare for different instances of the basic framework and different interpretations of the concept of social welfare itself. In particular, we show how certain classes of deals are both sufficient and necessary to guarantee that a socially optimal allocation of resources will be reached eventually.

Computing argumentation in logic programming

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 non-monotonic reasoning that can also be formulated via argumentation can be given new semantics, by a direct extension of the logic programming semantics. In this paper we develop an abstract computational framework where various argumen-tation semantics can be computed via diierent parametric variations of a simple basic proof theory. This proof theory is given in terms of derivations of trees where each node in a tree contains an argument (or attack) against its corresponding parent node. The proposed proof theory, deened here for the case of logic programming, generalises directly to other logics for non-monotonic reasoning that can also be formalised via argumentation. The abstract proof theory forms the basis for developing concrete top-down proof procedures for query evaluation. These proof procedures are obtained by adopting speciic search strategies and ways of computing attacks in the particular argumentation framework. For logic programming these procedures can be seen as a generalisation of the Eshghi-Kowalski abductive proof procedure that in turn generalises SLDNF. This is an extended and revised version of the earlier paper 46].

A Game-Theoretic Measure of Argument Strength for Abstract Argumentation

Abstract argumentation (Dung 1995) is a theory of dialectic that allows us to formalise and study various notions of argument acceptability. We depart from this standard approach and formalise a measure of argument strength by applying the concept of value of a game, as defined in Game Theory (von Neumann 1928). The measure thus obtained satisfies a number of intuitively appealing properties that can be derived mathematically from the minimax theorem.

On the computational complexity of assumption-based argumentation for default reasoning

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 analyse the computational complexity of credulous and sceptical reasoning under the semantics of admissible and preferred arguments for (the propositional variant of) the instances of the abstract framework capturing theorist, circumscription, logic programming, default logic, and autoepistemic logic. Although the new semantics have been tacitly assumed to mitigate the computational hardness of default reasoning under the standard semantics of stable extensions, we show that in many cases reasoning under the admissibility and preferability semantics is computationally harder than under the standard semantics. In particular, in the case of autoepistemic logic, sceptical reasoning under preferred arguments is located at the fourth level of the polynomial hierarchy, whereas the same form of reasoning under stable extensions is located at the second level.

An Abductive Logic Programming Architecture for Negotiating Agents

In this paper, we present a framework for agent negotiation based on abductive logic programming. The framework is based on an existing architecture for logic-based agents, and extends it by accommodating dialogues for negotiation. As an application of negotiating agents, we propose a resource-exchanging problem. The innovative contribution of this work is in the definition of an operational model, including an agent cycle and dialogue cycle, and in the results that apply in the general case of abductive agents and in the specific case of a class of agent systems.