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46
Graduality in argumentation
 Journal of Artificial Intelligence Research
, 1998
"... Argumentation is based on the exchange and valuation of interacting arguments, followed by the selection of the most acceptable of them (for example, in order to take a decision, to make a choice). Starting from the framework proposed by Dung in 1995, our purpose is to introduce “graduality ” in the ..."
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Argumentation is based on the exchange and valuation of interacting arguments, followed by the selection of the most acceptable of them (for example, in order to take a decision, to make a choice). Starting from the framework proposed by Dung in 1995, our purpose is to introduce “graduality ” in the selection of the best arguments, i.e. to be able to partition the set of the arguments in more than the two usual subsets of “selected ” and “nonselected ” arguments in order to represent different levels of selection. Our basic idea is that an argument is all the more acceptable if it can be preferred to its attackers. First, we discuss general principles underlying a “gradual ” valuation of arguments based on their argumentation system. Then, we introduce “graduality ” in the concept of acceptability of arguments. We propose new acceptability classes and a refinement of existing classes taking advantage of an available “gradual ” valuation. 1.
Argument diagramming in logic, law and artificial intelligence
 Knowledge Engineering Review
, 2007
"... In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated — informal logic, argumentation theory, evidence law and legal reasoning — but also more recent work in applying and developing it in computer science an ..."
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In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated — informal logic, argumentation theory, evidence law and legal reasoning — but also more recent work in applying and developing it in computer science and artificial intelligence (AI). Beginning with a simple example of an everyday argument, we present an analysis of it visualized as an argument diagram constructed using a software tool. In the context of a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyse and work with argumentation in law, philosophy and (AI). 1
A Logic Programming Framework for Possibilistic Argumentation: Formalization and Logical Properties 1
"... In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argumentbased frameworks on the basis of different variants of l ..."
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In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argumentbased frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (PDeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on Gödel fuzzy logic. One of the applications of PDeLP is providing an intelligent agent with nonmonotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two nonmonotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studied.
Joint Probabilities
"... When combining information from multiple sources and attempting to estimate the probability of a conclusion, we often find ourselves in the position of knowing the probability of the conclusion conditional on each of the individual sources, but we have no direct information about the probability of ..."
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When combining information from multiple sources and attempting to estimate the probability of a conclusion, we often find ourselves in the position of knowing the probability of the conclusion conditional on each of the individual sources, but we have no direct information about the probability of the conclusion conditional on the combination of sources. The probability calculus provides no way of computing such joint probabilities. This paper introduces a new way of combining probabilistic information to estimate joint probabilities. It is shown that on a particular conception of objective probabilities, clear sense can be made of secondorder probabilities (probabilities of probabilities), and these can be related to combinatorial theorems about proportions in finite sets as the sizes of the sets go to infinity. There is a rich mathematical theory consisting of such theorems, and the theorems generate corresponding theorems about secondorder probabilities. Among the latter are a number of theorems to the effect that certain inferences from probabilities to probabilities, although not licensed by the probability calculus, have probability 1 of producing correct results. This does not mean that they will always produce correct results, but the set of cases in which the inferences go wrong form a set of measure 0. Among these
Formalizing Argumentative Reasoning in a Possibilistic Logic Programming Setting with Fuzzy Unification ⋆
"... Possibilistic Defeasible Logic Programming (PDeLP) is a logic programming language which combines features from argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at the objectlanguage level. In spite of its expressive power, an important limitatio ..."
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Possibilistic Defeasible Logic Programming (PDeLP) is a logic programming language which combines features from argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at the objectlanguage level. In spite of its expressive power, an important limitation in PDeLP is that imprecise, fuzzy information cannot be expressed in the object language. One interesting alternative for solving this limitation is the use of PGL +, a possibilistic logic over Gödel logic extended with fuzzy constants. Fuzzy constants in PGL + allow expressing disjunctive information about the unknown value of a variable, in the sense of a magnitude, modeled as a (unary) predicate. The aim of this article is twofold: firstly, we formalize DePGL +, a possibilistic defeasible logic programming language that extends PDeLP through the use of PGL + in order to incorporate fuzzy constants and a fuzzy unification mechanism for them. Secondly, we propose a way to handle conflicting arguments in the context of the extended framework. Key words: Possibilistic logic, fuzzy constants, fuzzy unification, defeasible argumentation, warrant computation
The Logicist Manifesto: At Long Last Let LogicBased AI Become a Field Unto Itself
 Journal of Applied Logic
, 2008
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A configurable reteoo engine for reasoning with different types of imperfect information
 IEEE Trans. Knowl. Data Eng
"... Abstract—The RETE algorithm is a very efficient option for the development of a rulebased system, but it supports only boolean, first order logic. Many realworld contexts, instead, require some degree of vagueness or uncertainty to be handled in a robust and efficient manner, imposing a tradeoff ..."
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Abstract—The RETE algorithm is a very efficient option for the development of a rulebased system, but it supports only boolean, first order logic. Many realworld contexts, instead, require some degree of vagueness or uncertainty to be handled in a robust and efficient manner, imposing a tradeoff between the number of rules and the cases that can be handled with sufficient accuracy. Thus, in the first part of the paper, an extension of RETE networks is proposed, capable of handling a more general inferential process, which actually includes several types of schemes for reasoning with imperfect information. In particular, the architecture depends on a number of configuration parameters which could be set by the user, individually or as a whole for the entire rule base. The second part, then, shows how an appropriate combination of parameters can be used to emulate some of the most common, specialized engines: 3valued logic, classical certainty factors, fuzzy, manyvalued logic and Bayesian networks. Index Terms—Inference engines, nonmonotonic reasoning and belief revision, rulebased processing, uncertainty, “fuzzy ” and probabilistic reasoning. Ç 1
Threat, reward and explanatory arguments: generation and evaluation
, 2004
"... Current logicbased handling of arguments has mainly focused on explanationoriented purposes in presence of inconsistency, so only one type of argument has been considered. Several argumentation frameworks have then been proposed for generating and evaluating such arguments. However, recent works ..."
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Current logicbased handling of arguments has mainly focused on explanationoriented purposes in presence of inconsistency, so only one type of argument has been considered. Several argumentation frameworks have then been proposed for generating and evaluating such arguments. However, recent works on argumentationbased negotiation have emphasized different other types of arguments such as threats, rewards, appeals. The purpose of this paper is to provide a logical setting which encompasses the classical argumentationbased framework and handles the new types of arguments. More precisely, we give the logical definitions of these arguments and their weighting systems. These definitions take into account that negotiation dialogues involve not only agents ’ beliefs (of various strengths), but also their goals (having maybe different priorities), as well as the beliefs on the goals of other agents. In other words, from the different belief and goal bases maintained by agents, all the possible threats, rewards, explanations, appeals which are associated with them can be generated.
Three Senses of ‘Argument
 Proc. Workshop Argumentation and Nonmonotonic Reasoning (ArgNMR
"... Abstract. In AI approaches to argumentation, different senses of argument are often conflated. We propose a threelevel distinction between arguments, cases, and debates. This allows for modularising issues within levels and identifying systematic relations between levels. Arguments, comprised of ru ..."
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Abstract. In AI approaches to argumentation, different senses of argument are often conflated. We propose a threelevel distinction between arguments, cases, and debates. This allows for modularising issues within levels and identifying systematic relations between levels. Arguments, comprised of rules, facts, and a claim, are the basic units; they instantiate argument schemes; they have no subarguments. Cases are sets of arguments supporting a claim. Debates are a set of arguments in an attack relation; they include cases for and against a particular claim. Critical questions, which depend on the argument schemes, are used to determine the attack relation between arguments. In a debate, rankings on arguments or argument relations are given as components based on features of argument schemes. Our analysis clarifies the role and contribution of distinct approaches in the construction of rational debate. It identifies the source of properties used for evaluating the status of arguments in
P.: Merging argumentation systems
 In: AAAI 2005
, 2005
"... In this paper, we address the problem of deriving sensible information from a collection of argumentation systems coming from different agents. A general framework for merging argumentation systems from Dung’s theory of argumentation is presented. Each argumentation system gives both a set of arg ..."
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In this paper, we address the problem of deriving sensible information from a collection of argumentation systems coming from different agents. A general framework for merging argumentation systems from Dung’s theory of argumentation is presented. Each argumentation system gives both a set of arguments and the way they interact (i.e. attack or nonattack) according to the corresponding agent. The aim is to define the argument system (or the set of argument systems) that best represents the group. Our framework is general enough to handle the case when agents do not share the same set of arguments. Merging argumentation systems is shown as a valuable approach for defining (sets of) arguments acceptable by the group.