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 pro...

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, i. e. the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent’s knowledge and for providing an argumentation based reasoning mechanism to agents.

This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but efficient formalism for nonmonotonic reasoning based on rules and priorities. The transformations described in this paper have two main benefits: on one hand they can be used as a theoretical tool that leads to a deeper understanding of the formalism, and on the other hand they have been used in the development of an efficient implementation of defeasible logic

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.

For many years, the non-monotonic reasoning commu-nity has focussed on highly expressive logics. Such logics have tumed out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic: a query answering system employing a backward-chaining approach, and a forward-chaining implementation that computes all conclusions. Our experimental evaluation demonstrates that the systems can deal with large theories (up to hundreds of thousands of rules). We show that defea-sible logic has linear complexity, which contrasts markedly with most other non-monotonic logics and helps to explain the impressive experimental results. We believe that defea-sible logic, with its eficiency and simplicity, is a good can-didate to be used as a modelling language for practical ap-plications, including modelling of regulations and business rules. 1

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable. 1 Introduction Mostwork in non-monotonicreasoning has focussed on languages for whichpropositional inference is not tractable. Sceptical default reasoning is \Pi p 2 -hard, even for very simple classes of default rules, as is sceptical autoepistemic reasoning and propositional circumscription. The complexity of sceptical inference from logic programs with negation-as-failure varies according to the semantics of negation. For both the stable model semantics and the Clark completion, sceptical inference is co-NPhard. See [13, 9] for more details. Although such languages are very expressive, and this expressiveness has been exploited in answer-set progra...

Logics for knowledge representation suffer from overspecialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several logics and, when necessary, combine the representations. In general, such an approach results in a very difficult problem of combination. However, if we can choose the logics from a uniform framework then the problem of combining them is greatly simplified. In this paper, we develop such a framework for defeasible logics. It supports all defeasible logics that satisfy a strong negation principle. We use logic meta-programs as the basis for the framework.

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This paper presents a new model of agency, called the KGP (Knowledge, Goals and Plan) model. This draws from the classic BDI model and proposes a hierarchical agent architecture with a highly modular structure that synthesises various reasoning and sensing capabilities of the agent in an open and dynamic environment. The novel features of the model include: its innovative use of Computational Logic (CL) in a way that facilitates both the formal analysis of the model and its computational realisability directly from the high-level specification of the agents (a first prototype for the development of KGP agents exists, based upon a correct computational counterpart of the model), the modular separation of concerns and flexibility afforded by the model in designing heterogeneous agents and in developing independently the various components of an agent, and the declarative agent control provided through a context-sensitive cycle CL theory component that regulates the agent's operational behaviour, according to the current circumstances of operation, thus breaking away from the conventional one-size-fits-all control of operation.

Recently there has been increased interest in logic programming-based default reasoning approaches which are not using negation-as-failure in their object language. Instead, default reasoning is modelled by rules and a priority relation among them. In this paper we compare the expressive power of two approaches in this family of logics: Defeasible Logic, and sceptical LPwNF. Our results show that the former has a strictly stronger expressive power. The difference is caused by the latter logic's failure to capture the idea of teams of rules supporting a specific conclusion.