This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...) to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...) century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

The notion of similarity has been studied in many areas of Computer Science; in a general sense, this concept is defined to provide a measure of the semantic equivalence between two pieces of knowl...

We present an interdisciplinary approach to argumentation combining logical, probabilistic, and psychological perspectives. We investigate logical attack principles which relate attacks among claims with logical form. For example, we consider the principle that an argument that attacks another argument claiming A triggers the existence of an attack on an argument featuring the stronger claim A ∧ B. We formulate a number of such principles pertaining to conjunctive, disjunctive, negated, and implicational claims. Some of these attack principles seem to be prima (...) facie more plausible than others. To support this intuition, we suggest an interpretation of these principles in terms of coherent conditional probabilities. This interpretation is naturally generalized from qualitative to quantitative principles. Specifically, we use our probabilistic semantics to evaluate the rationality of principles which govern the strength of argumentative attacks. In order to complement our theoretical analysis with an empirical perspective, we present an experiment with students of the TU Vienna ( n = 139) which explores the psychological plausibility of selected attack principles. We also discuss how our qualitative attack principles relate to well-known types of logical argumentation frameworks. Finally, we briefly discuss how our approach relates to the computational argumentation literature. (shrink)

Argumentation has been an important topic in knowledge representation, reasoning and multi-agent systems during the last twenty years. In this paper, we propose a new abstract framework where arguments are associated with a strength, namely a quantitative information which is used to determine whether an attack between arguments succeeds or not. Our Strength-based Argumentation Framework combines ideas of Preference-based and Weighted Argumentation Frameworks in an original way, which permits to define acceptability semantics sensitive to the existence of accruals between arguments. (...) The question of accruals arises in situations where several arguments defending the same position against another argument are unable to individually defeat this argument, but could do it collectively if they combine their strengths. We investigate some of the theoretical and computational properties of our new framework and semantics, and present a reasoning algorithm that is based on a translation of the problem into pseudo-boolean constraint satisfaction. This paper proposes an intuitive framework which allows strength compensations in an argumentation context where attacks may not succeed, completed by an approach which detects accruals throughout the reasoning process without requiring the elicitation of all compensatory combinations of arguments as an input. (shrink)

Dung’s argumentation frameworks have been applied for over twenty years to the analysis of argument justification. This representation focuses on arguments and the attacks among them, abstracting away from other features like the internal structure of arguments, the nature of utterers, the specifics of the attack relation, etc. The model is highly attractive because it reduces most of the complexities involved in argumentation processes. It can be applied to different settings, like the argument evaluation of an individual agent or the (...) case of dialectic disputes between two agents (pro and con), or even in multi-agent collective argumentation. The latter case involves agents with possibly different arguments and/or opinions on how to evaluate them, leading to the possibility of considering multiple sets of arguments and attack relations. Two basic questions can be asked here, namely ‘what to aggregate’ and ‘how to aggregate’. The former concerns what kinds of entities do the agents intend to choose (arguments, attacks, assessments, etc.), while the second one focuses on which aggregation mechanisms yield rational choices (voting on arguments, merging procedures to obtain a common argumentation framework, deliberation processes, etc.). In particular, the question about the rationality of a collective argument choice relates this topic to Social Choice and Judgment Aggregation theories, while its associated strategic issues relate it to Game Theory. The research efforts on the disparate problems elicited by collective argumentation have generated a considerable corpus of literature that deserves an orderly evaluation. This survey is intended as a contribution to that end. (shrink)

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework, the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last (...) years. In this paper, we survey approaches that allow to express information like “There may be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future. (shrink)

Argumentation has been an important topic in knowledge representation, reasoning and multi-agent systems during the last twenty years. In this paper, we propose a new abstract framework where arguments are associated with a strength, namely a quantitative information which is used to determine whether an attack between arguments succeeds or not. Our Strength-based Argumentation Framework (StrAF) combines ideas of Preference-based and Weighted Argumentation Frameworks in an original way, which permits to define acceptability semantics sensitive to the existence of accruals between (...) arguments. The question of accruals arises in situations where several arguments defending the same position (but from different points of view) against another argument are unable to individually defeat this argument, but could do it collectively if they combine their strengths. We investigate some of the theoretical and computational properties of our new framework and semantics, and present a reasoning algorithm that is based on a translation of the problem into pseudo-boolean constraint satisfaction. This paper proposes an intuitive framework which allows strength compensations in an argumentation context where attacks may not succeed, completed by an approach which detects accruals throughout the reasoning process without requiring the elicitation of all compensatory combinations of arguments as an input. (shrink)

In this paper, we propose an argumentation formalism that allows for both deductive and abductive argumentation, where ‘deduction’ is used as an umbrella term for both defeasible and strict ‘forward’ inference. Our formalism is based on an extended version of our previously proposed information graph formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. In the current version, we consider additional types of information such as abstractions which allow domain experts (...) to be more expressive in stating their knowledge, where we identify and impose constraints on the types of inferences that may be performed with the different types of information. A new notion of attack is defined that captures a crucial aspect of abductive reasoning, namely that of competition between abductively inferred alternative explanations. Our argumentation formalism generates an abstract argumentation framework and thus allows arguments to be formally evaluated. We prove that instantiations of our argumentation formalism satisfy key rationality postulates. (shrink)

Persuasion is an activity that involves one party trying to induce another party to believe something or to do something. It is an important and multifaceted human facility. Obviously, sales and ma...

The concept of conductive argument weight was developed by Carl Wellman and later by Trudy Govier. This concept has received renewed attention recently from another informal logician, Robert C. Pinto. Argument weight has also been addressed in recent years by theorists in AI & Law. I argue from a non-technical perspective that some aspects of AI & Law’s approach to argument weight can be usefully applied to the issues addressed by Pinto. I also relate some of these issues to the (...) work of argument theorist Harald Wohlrapp. (shrink)

Argumentation is a form of reasoning where a claim is accepted or rejected according to the analysis of the arguments for and against it; furthermore, it provides a reasoning mechanism able to handle contradictory, incomplete and uncertain information in real-world situations. We combine Bipolar Argumentation Frameworks (an extension of Dung’s work) with an Algebra of Argumentation Labels modeling two independent types of interaction between arguments, representing meta-information associated with arguments, and introducing an acceptability notion that will give more information for (...) arguments acceptability. (shrink)

This paper presents a novel argumentation framework to support Issue-Based Information System style debates on design alternatives, by providing an automatic quantitative evaluation of the positions put forward. It also identifies several formal properties of the proposed quantitative argumentation framework and compares it with existing non-numerical abstract argumentation formalisms. Finally, the paper describes the integration of the proposed approach within the design Visual Understanding Environment software tool along with three case studies in engineering design. The case studies show the potential (...) for a competitive advantage of the proposed approach with respect to state-of-the-art engineering design methods. (shrink)

Abstract. The notion of similarity has been studied in many areas of Computer Science; in a general sense, this concept is defined to provide a measure of the semantic equivalence between two pieces of knowledge, expressing how “close” their meaning can be regarded. In this work, we study similarity as a tool useful to improve the representation of arguments, the interpretation of the relations between arguments, and the semantic evaluation associated with the arguments in the argumentative process. In this direction, (...) we present a novel mechanism to determine the similarity between two arguments based on descriptors representing particular aspects associated with these arguments. This mechanism involves a comparison process influenced by the context in which the process develops, where this context provides the relevant aspects that need to be analyzed in the application domain. Then, we use this similarity measure as a quantity to compute the result of attacks and supports in the argumentation process. These valuations, applied to a Bipolar Argumentation Frameworks, allowed us to refine the argument relations, providing the tools to establish a family of new argumentation semantics that considers the similarity between arguments as a crucial part for the argumentation process. (shrink)