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Argumentative Logics: Reasoning With Classically Inconsistent Information
, 1995
"... Classical logic has many appealing features for knowledge representation and reasoning. But unfortunately it is flawed when reasoning about inconsistent information, since anything follows from a classical inconsistency. This problem is addressed by introducing the notions of "argument" an ..."
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Cited by 33 (1 self)
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Classical logic has many appealing features for knowledge representation and reasoning. But unfortunately it is flawed when reasoning about inconsistent information, since anything follows from a classical inconsistency. This problem is addressed by introducing the notions of "argument" and of "acceptability" of an argument. These notions are used to introduce the concept of "argumentative structures". Each definition of acceptability selects a subset of the set of arguments, and an argumentative structure is a subset of the power set of arguments. In this paper, we consider, in detail, a particular argumentative structure, where each argument is defined as a classical inference together with the applied premisses. For such arguments, a variety of definitions of acceptability are provided, the properties of these definitions are explored, and their inter-relationship described. The definitions of acceptability induce a family of logics called argumentative logics which we explore. The ...
A Review of Uncertainty Handling Formalisms
, 1998
"... Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one ..."
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Cited by 24 (1 self)
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Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.
Cost-bounded argumentation
- International Journal of Approximate Reasoning
"... The purpose of this paper is to present new computational techniques for probabilistic argumentation systems. It shows that instead of computing intractable large sets of arguments, it is also possible to find good approximations of the exact solutions in reasonable time. The technique presented is ..."
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Cited by 24 (14 self)
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The purpose of this paper is to present new computational techniques for probabilistic argumentation systems. It shows that instead of computing intractable large sets of arguments, it is also possible to find good approximations of the exact solutions in reasonable time. The technique presented is based on cost functions, which are used to measure the relevance of arguments.
A generalization of dung’s abstract framework for argumentation: Arguing with sets of attacking arguments
- In Proc. 3rd Int. Workshop on Argumentation in Multi-agent Systems
, 2006
"... Abstract. One of the most widely studied systems of argumentation is the one described by Dung in a paper from 1995. Unfortunately, this framework does not allow for joint attacks on arguments, which we argue must be required of any truly abstract argumentation framework. A few frameworks can be sai ..."
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Cited by 23 (2 self)
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Abstract. One of the most widely studied systems of argumentation is the one described by Dung in a paper from 1995. Unfortunately, this framework does not allow for joint attacks on arguments, which we argue must be required of any truly abstract argumentation framework. A few frameworks can be said to allow for such interactions among arguments, but for various reasons we believe that these are inadequate for modelling argumentation systems with joint attacks. In this paper we propose a generalization of the framework of Dung, which allows for sets of arguments to attack other arguments. We extend the semantics associated with the original framework to this generalization, and prove that all results in the paper by Dung have an equivalent in this more abstract framework. 1
Fusion in logic: A brief overview
- in Proceedings of the 4th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU'97, LNCS 1244
, 1997
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Towards Higher Impact Argumentation
, 2004
"... 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. An example is the framework by Besnard and Hunter that is based on classical logic and in which an argument ..."
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Cited by 22 (1 self)
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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. An example is the framework by Besnard and Hunter that is based on classical logic and in which an argument (obtained from a knowledgebase) is a pair where the first item is a minimal consistent set of formulae that proves the second item (which is a formula). In the framework, the only counter-arguments (defeaters) that need to be taken into account are canonical arguments (a form of minimal undercut) . Argument trees then provide a way of exhaustively collating arguments and counter-arguments. A problem with this set up is that some argument trees may be "too big" to have sufficient impact. In this paper, we address the need to increase the impact of argumentation by using pruned argument trees. We formalize this in terms of how arguments resonate with the intended audience of the arguments. For example, if a politician wants to make a case for raising taxes, the arguments used would depend on what is important to the audience: Arguments based on increased taxes are needed to pay for improved healthcare would resonate better with an audience of pensioners, whereas arguments based on increased taxes are needed to pay for improved transport infrastructure would resonate better with an audience of business executives. By
Evaluating significance of inconsistencies
- In Proceedings of the 18th International Joint Conference on Artificial Intellignce (IJCAI’03
, 2003
"... Inconsistencies frequently occur in knowledge about the real-world. Some of these inconsistencies may be more significant than others, and some knowledgebases (sets of formulae) may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, a ..."
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Cited by 22 (11 self)
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Inconsistencies frequently occur in knowledge about the real-world. Some of these inconsistencies may be more significant than others, and some knowledgebases (sets of formulae) may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap’s four-valued logic, and unlike other paraconsistent logics, allows the connectives to appear to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasi-classical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a measure of significance of inconsistencies in each knowledgebase. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge. 1
Hybrid Argumentation Systems for Structured News Reports
- Knowledge Engineering Review
, 2001
"... Numerous argumentation systems have been proposed in the literature. Yet there often appears to be a shortfall between proposed systems and possible applications. In other words, there seems to be a need for further development of proposals for argumentation systems before they can be used widely in ..."
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Cited by 19 (4 self)
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Numerous argumentation systems have been proposed in the literature. Yet there often appears to be a shortfall between proposed systems and possible applications. In other words, there seems to be a need for further development of proposals for argumentation systems before they can be used widely in decision-support or knowledge management. We believe that this shortfall can be bridged by taking a hybrid approach. Whilst formal foundations are vital, systems that incorporate some of the practical ideas found in some of the informal approaches may make the resulting hybrid systems more useful. In informal approaches, there is often an emphasis on using graphical notation with symbols that relate more closely to the real-world concepts to be modelled. There may also be the incorporation of an argument ontology oriented to the user domain. Furthermore, in informal approaches there can be greater consideration of how users interact with the models, such as allowing users to edit arguments and to weight influences on graphs representing arguments. In this paper, we discuss some of the features of argumentation, review some key formal argumentation systems, identify some of the strengths and weaknesses of these formal proposals, and finally consider some ways to develop formal proposals to give hybrid argumentation systems. To focus our discussions, we will consider some applications, in particular an application in analysing structured news reports.
Normative argumentation and qualitative probability
, 1996
"... Abstract. In recent years there has been a spate of papers describing systems for plausible reasoning which do not use numerical measures of uncertainty. Some of the most successful of these have been systems for argumentation, and there are advantages in considering the condi-tions under which such ..."
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Cited by 18 (7 self)
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Abstract. In recent years there has been a spate of papers describing systems for plausible reasoning which do not use numerical measures of uncertainty. Some of the most successful of these have been systems for argumentation, and there are advantages in considering the condi-tions under which such systems are normative. This paper discusses an extension to previous work on normative argumentation, exploring the properties of a particular normative approach to argumentation and sug-gesting some uses of it. 1
Reasoning with Contradictory Information using Quasi-classical Logic
- Journal of Logic and Computation
, 1999
"... The proof theory of quasi-classical logic (QC logic) allows the derivation of non-trivializable classical inferences from inconsistent information. A non-trivializable, or paraconsistent, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be m ..."
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Cited by 18 (4 self)
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The proof theory of quasi-classical logic (QC logic) allows the derivation of non-trivializable classical inferences from inconsistent information. A non-trivializable, or paraconsistent, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in a classical manner. Here we motivate the need for QC logic, present a proof theory, and semantics for the logic, and compare it to other paraconsistent logics. 1 Introduction Intellectual activities usually involve reasoning with different perspectives. For example, consider negotiation, learning, or merging multiple opinions. Central to reasoning with different perspectives is the issue of handling inconsistencies. Maintaining absolute consistency is not always possible. Often it is not even desirable since this can unnecessarily constrain the intellectual activity, and ...
