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logic-based argumentation with existential rules

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2017年 90卷 76-106页

作者： Arioua, Abdallah Croitoru, Madalina Vesic, Srdjan Univ Claude Bernard Lyon 1 LIRIS CNRS Lyon France Univ Montpellier 2 LIRMM INRIA Montpellier France CNRS CRIL Lens France Univ Artois Lens France

In this paper we are interested in the use of argumentation for handling inconsistency in inconsistent knowledge bases expressed with existential rules. We propose an instantiation of an argumentation framework and demonstrate it is coherent, relatively grounded and non-trivial, therefore satisfying the rationality postulates from the literature. We demonstrate how argumentation semantics relate to the state of the art of handling inconsistency in this setting, allowing us to propose the first dialectical proof in the literature for a given semantics. (C) 2017 Elsevier Inc. All rights reserved.

关键词： logic-based argumentation Existential rules Universal acceptance Dialectical proof theory

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Complexity Classifications for logic-based argumentation

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ACM TRANSACTIONS ON COMPUTATIONAL logic 2014年第3期15卷 1–20页

作者： Creignou, Nadia Egly, Uwe Schmidt, Johannes Aix Marseille Univ CNRS LIF UMR 7279 F-13000 Marseille France Vienna Univ Technol Inst Informat Syst E184 3 A-1040 Vienna Austria Linkoping Univ Dept Comp & Informat Sci S-58183 Linkoping Sweden

We consider logic-based argumentation in which an argument is a pair (Phi, alpha), where the support Phi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by Delta) that entails the claim alpha (a formula). We study the complexity of three central problems in argumentation: the existence of a support Phi subset of Delta, the verification of a support, and the relevance problem (given psi, is there a support Phi such that psi is an element of Phi?). When arguments are given in the frill language of propositional logic, these problems are computationally costly tasks: the verification problem is DP-complete;the others are Sigma(P)(2)-complete. We study these problems in Schaefer's famous framework where the considered propositional formulae are in generalized conjunctive normal form. This means that formulae are conjunctions of constraints built upon a fixed finite set of Boolean relations Gamma (the constraint language). We show that according to the properties of this language Gamma, deciding whether there exists a support for a claim in a given knowledge base is either polynomial, NP-complete, coNP-complete, or Sigma(P)(2)-complete. We present a dichotomous classification, P or DP-complete, for the verification problem and a trichotomous classification for the relevance problem into either polynomial, NP-complete, or Sigma(P)(2)-complete. These last two classifications are obtained by means of algebraic tools.

关键词： Theory Computational complexity generalized satisfiability logic-based argumentation Schaefer

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Implementing crash-resistance and non-interference in logic-based argumentation

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JOURNAL OF logic AND COMPUTATION 2015年第2期25卷 303-333页

作者： Wu, Yining Podlaszewski, Mikolaj Univ Luxembourg Comp Sci & Commun Interdisciplinary Ctr Secur Rel L-1359 Luxembourg Luxembourg

Over the last decennia, many systems for formal argumentation have been defined. The problem, however, is that these systems do not always satisfy reasonable properties. In the current study, we focus on the particular property that a conflict between two arguments should not keep other unrelated arguments from becoming justified. Although this property appears obvious, it is in fact violated by several existing argumentation formalisms. In this article we examine what exactly goes wrong and how things can be improved.

关键词： Formal argumentation logic-based argumentation postulates

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Parameterized Complexity of logic-based argumentation in Schaefer's Framework

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ACM TRANSACTIONS ON COMPUTATIONAL logic 2023年第3期24卷 1-25页

作者： Mahmood, Yasir Meier, Arne Schmidt, Johannes Leibniz Univ Hannover Inst Theoret Informat Appelstr 9A D-30167 Hannover Germany Jonkoping Univ Sch Engn Dept Comp Sci & Informat Gjuterigatan 5 S-55111 Jonkoping Sweden

argumentation is a well-established formalism dealing with conflicting information by generating and comparing arguments. It has been playing a major role in AI for decades. In logic-based argumentation, we explore the internal structure of an argument. Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this article, we study the propositional variants of the following three computational tasks studied in argumentation: ARG (exists a support for a given claim with respect to a given set of formulas), ARG-Check (is a given set a support for a given claim), and ARG-Rel (similarly as ARG plus requiring an additionally given formula to be contained in the support). ARG-Check is complete for the complexity class DP, and the other two problems are known to be complete for the second level of the polynomial hierarchy (Creignou et al. 2014 and Parson et al., 2003) and, accordingly, are highly intractable. Analyzing the reason for this intractability, we perform a two-dimensional classification: First, we consider all possible propositional fragments of the problem within Schaefer's framework (STOC 1978) and then study different parameterizations for each of the fragments. We identify a list of reasonable structural parameters (size of the claim, support, knowledge base) that are connected to the aforementioned decision problems. Eventually, we thoroughly draw a fine border of parameterized intractability for each of the problems showing where the problems are fixed-parameter tractable and when this exactly stops. Surprisingly, several cases are of very high intractability (para-NP and beyond).

关键词： Parameterized complexity logic-based argumentation Schaefer's framework

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Complexity of logic-based argumentation in Schaefer's framework

Complexity of logic-based argumentation in Schaefer's framew...

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4th Conference on Computational Models of Argument (COMMA)

作者： Creignou, Nadia Egly, Uwe Schmidt, Johannes Aix Marseille Univ LIF UMR CNRS 7279 163 Ave Luminy F-13288 Marseille France Tech Univ Wien Inst fur Informat Syst Vienna Austria

ISBN: (纸本)9781614991113;9781614991106

We consider logic-based argumentation in which an argument is a pair (Phi, alpha), where the support Phi is a minimal consistent set of formulae of a given knowledge base that entails the formula alpha. We study the complexity of two different problems: the existence of a support and the verification of the validity of an argument. When arguments are given in the full language of propositional logic these problems are computationally costly tasks, they are respectively Sigma(P)(2)- and DP-complete. We study these problems in Schaefer's famous framework. We consider the case where formulae are taken from a class of formulae in generalized conjunctive normal form. This means that the propositional formulae considered are conjunctions of constraints taken from a fixed finite language Gamma. We show that according to the properties of this language Gamma, deciding whether there exists a support for a claim in a given knowledge base is either polynomial, NP-complete, coNP-complete or Sigma(P)(2)-complete. We also obtain a dichotomous classification, P or DP-complete, for the verification problem.

关键词： complexity of argumentation logic-based argumentation Schaefer generalized satisfiability

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Properties and complexity in feasible logic-based argumentation for electronic commerce 8th

Properties and complexity in feasible logic-based argumentat...

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8th Ibero-American Conference on Artifical Intelligence (IBERAMIA 02)

作者： Brito, L Neves, J Univ Minho Dept Informat P-4719 Braga Portugal

ISBN: (纸本)354000131X

logic-based argumentation (LBA) exhibits unique properties and advantages over other kinds of argumentation proceedings, namely: the adequacy to logic-based pre-argument reasoning, similarity to the human reasoning process, reasoning with incomplete information and argument composition and extension. logic enables a formal specification to be built and a quick prototype to be developed. In order for LBA to achieve feasibility in Electronic Commerce scenarios, a set of properties must be present: self-support, correctness, conjugation, temporal containment and acyclicity. At the same time, LBA is shown to achieve stability in argument exchange (guaranteed success problem) and, depending on the definition of success, computational efficiency at each round (success problem).

关键词： logic-based argumentation electronic commerce success problem guaranteed success problem

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Explanatory dialogues with argumentative faculties over inconsistent knowledge bases

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EXPERT SYSTEMS WITH APPLICATIONS 2017年 80卷 244-262页

作者： Arioua, Abdallah Buche, Patrice Croitoru, Madalina French Natl Inst Agr Res UMR IATE Pl Pierre Viala F-34060 Montpellier France Univ Montpellier LIRMM 161 Rue ADA F-34392 Montpellier 5 France

We introduce a formal model of explanatory dialogue called EDS. We extend this model by including argumentation capacities to facilitate knowledge acquisition in inconsistent knowledge bases. To prove the relevance of such model we provide the DALEK (DiALectical Explanation in Knowledge-bases) framework that implements this model. We show the usefulness of the framework on a real-world application in the domain of Durum Wheat sustainability improvement within the ANR (French National Agency) funded Dur-Dur project. The preliminary pilot evaluation of the framework with agronomy experts gives a promising indication on the impact of explanation dialogues on the improvement of the knowledge's content. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Knowledge representation and reasoning Explanation argumentation Dialogue Formal dialectics logic-based argumentation

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A probabilistic approach to modelling uncertain logical arguments

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2013年第1期54卷 47-81页

作者： Hunter, Anthony UCL Dept Comp Sci London WC1E 6BT England

argumentation can be modelled at an abstract level using a directed graph where each node denotes an argument and each arc denotes an attack by one argument on another. Since arguments are often uncertain, it can be useful to quantify the uncertainty associated with each argument. Recently, there have been proposals to extend abstract argumentation to take this' uncertainty into account. This assigns a probability value for each argument that represents the degree to which the argument is believed to hold, and this is then used to generate a probability distribution over the full subgraphs of the argument graph, which in turn can be used to determine the probability that a set of arguments is admissible or an extension. In order to more fully understand uncertainty in argumentation, in this paper, we extend this idea by considering logic-based argumentation with uncertain arguments. This is based on a probability distribution over models of the language, which can then be used to give a probability distribution over arguments that are constructed using classical logic. We show how this formalization of uncertainty of logical arguments relates to uncertainty of abstract arguments, and we consider a number of interesting classes of probability assignments. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Computational models of argument Argument systems logic-based argumentation Probabilistic argumentation logical arguments Uncertain arguments

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An argumentation system for eco-efficient packaging material selection

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2015年 113卷 174-192页

作者： Tamani, Nouredine Mosse, Patricio Croitoru, Madalina Buche, Patrice Guillard, Valerie Guillaume, Carole Gontard, Nathalie INRIA GraphiK LIRMM F-34095 Montpellier 5 France UM2 INRA UMR IATE Montpellier France

Within the framework of the European project EcoBioCap (ECOefficient BIOdegradable Composite Advanced Packaging), aiming at conceiving the next generation of food packagings, we have designed an argumentation-based tool for management of conflicting viewpoints between preferences expressed by the involved parties (food and packaging industries, health authorities, consumers, waste management authority, etc.). The requirements and user preferences are modeled by several rules provided by the stakeholders expressing their viewpoints and expertise. based on these rules, the argumentation tool computes consensual preferences which are used to parameterize a flexible querying process of a packaging database to retrieve the most relevant solution to pack a given food. In this paper, we recall briefly the principles underlying the reasoning process, and we detail the main functionalities and the architecture of the argumentation tool. We cover the overall reasoning steps starting from formal representation of text arguments and ending by extraction of justified preferences which are sent to the database querying process. Finally, we detail its operational functioning through a real life case study to determine the justifiable choices between recyclable, compostable and biodegradable packaging materials based on stakeholders' arguments. (C) 2015 Elsevier B.V. All rights reserved.

关键词： logic-based argumentation argumentation tool Decision Support System Food packaging

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Algorithms for generating arguments and counterarguments in propositional logic

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2011年第6期52卷 672-704页

作者： Efstathiou, Vasiliki Hunter, Anthony UCL Dept Comp Sci London WC1E 6BT England

A common assumption for logic-based argumentation is that an argument is a pair (Phi, alpha) where Phi is minimal subset of the knowledgebase such that Phi is consistent and Phi entails the claim alpha. Different logics provide different definitions for consistency and entailment and hence give us different options for formalising arguments and counterarguments. The expressivity of classical propositional logic allows for complicated knowledge to be represented but its computational cost is an issue. In previous work we have proposed addressing this problem using connection graphs and resolution in order to generate arguments for claims that are literals. Here we propose a development of this work to generate arguments for claims that are disjunctive clauses of more than one disjunct, and also to generate counteraguments in the form of canonical undercuts (i.e. arguments that with a claim that is the negation of the conjunction of the support of the argument being undercut). (C) 2011 Elsevier Inc. All rights reserved.

关键词： logic-based argumentation Computational models of argument

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