Argument Graph Research Articles

Argumentation graphs with constraint-based reasoning for collaborative expertise

Collaborative processes are very important in telemedicine domain since they allow for making right decisions in complex situations with multidisciplinary staff. When modelling these collaborative processes, some inconsistencies can appear. In semantic modelling (conceptual graphs), these inconsistencies are verified using constraints. In this work, collaborative processes are represented using an argumentation system modelled in a conceptual graph formalism where inconsistencies could be particular bad attack relation between arguments. To overcome these inconsistencies, two solutions are proposed. The first one is to weight the arguments evolving in the argumentation system on the basis of the competencies of the health professionals and the credibility of the sources justifying their advice (arguments), and the second one is to model some law concepts as constraints in order to check their compliance of the collaborative process.

Cumulative Arguments in Artificial Intelligence and Informal Logic / Argumentos acumulativos en inteligencia artificial y lógica informal

We define a new type of argument structure specifically for modeling cumulative arguments and then show how this structure is general enough to simulate linked and convergent arguments. Argumentation schemes are associated with argument weighing functions in this language, where the weight of an argument can depend on the status (labeling) of its premises in an argument graph. Several key examples are used to illustrate the modeling of cumulative arguments, as well as linked and convergent arguments, with this approach. One hypothesis suggested by the analysis of these examples is that cumulative arguments can be treated in the same way as what is called argument accrual in artificial intelligence.

Experimental Assessment of Aggregation Principles in Argumentation-Enabled Collective Intelligence

On the Web, there is always a need to aggregate opinions from the crowd (as in posts, social networks, forums, etc.). Different mechanisms have been implemented to capture these opinions such as Like in Facebook, Favorite in Twitter, thumbs-up/-down, flagging, and so on. However, in more contested domains (e.g., Wikipedia, political discussion, and climate change discussion), these mechanisms are not sufficient, since they only deal with each issue independently without considering the relationships between different claims. We can view a set of conflicting arguments as a graph in which the nodes represent arguments and the arcs between these nodes represent the defeat relation. A group of people can then collectively evaluate such graphs. To do this, the group must use a rule to aggregate their individual opinions about the entire argument graph. Here we present the first experimental evaluation of different principles commonly employed by aggregation rules presented in the literature. We use randomized controlled experiments to investigate which principles people consider better at aggregating opinions under different conditions. Our analysis reveals a number of factors, not captured by traditional formal models, that play an important role in determining the efficacy of aggregation. These results help bring formal models of argumentation closer to real-world application.

Pareto optimality and strategy-proofness in group argument evaluation

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences.

Optimization of dialectical outcomes in dialogical argumentation

When informal arguments are presented, there may be imprecision in the language used, and so the audience may be uncertain as to the structure of the argument graph as intended by the presenter of the arguments. For a presenter of arguments, it is useful to know the audience's argument graph, but the presenter may be uncertain as to the structure of it. To model the uncertainty as to the structure of the argument graph in situations such as these, we can use probabilistic argument graphs. The set of subgraphs of an argument graph is a sample space. A probability value is assigned to each subgraph such that the sum is 1, thereby reflecting the uncertainty over which is the actual subgraph. We can then determine the probability that a particular set of arguments is included or excluded from an extension according to a particular Dung semantics. We represent and reason with extensions from a graph and from its subgraphs, using a logic of dialectical outcomes that we present. We harness this to define the notion of an argumentation lottery, which can be used by the audience to determine the expected utility of a debate, and can be used by the presenter to decide which arguments to present by choosing those that maximize expected utility. We investigate some of the options for using argumentation lotteries, and provide a computational evaluation.

An analysis of critical-link semantics with variable degrees of justification

This paper is to critically examines Pollock’s critical-link semantics with variable degrees of justification. Some possibly counterintuitive consequences of Pollock’s definition of degrees of justification are identified and a modified definition is proposed which avoids these consequences. Then the new solution is applied to the case of so-called presumptive defeat. A second contribution of the paper is to show how the modified semantics can be applied to the ASPIC+ framework: first the ASPIC+ framework is modified to allow for variable degrees of justification and then the modified way to compute these degrees is applied in a new notion of an argument graph

Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context

We examine a commonly suggested proof construction strategy from the mathematics education literature—that students first produce a graphical argument and then work to construct a verbal-symbolic proof based on that graphical argument. The work of students who produce such graphical arguments when solving proof construction tasks was analyzed to distill three activities that contribute to students’ successful translation of graphical arguments into verbal-symbolic proofs. These activities are called elaborating, syntactifying, and rewarranting. We analyze how engaging in these activities relates to students’ success in proof construction tasks. Additionally, we discuss how each individual activity contributes to the translation of a graphical argument into a verbal-symbolic proof.

A Note on the Noncollapsibility of Rate Differences and Rate Ratios.

It is well known that the odds ratio is noncollapsible, in the sense that conditioning on a covariate that is related to the outcome typically changes the size of the odds ratio, even if this covariate is unrelated to the exposure. The risk difference and risk ratio do not have this peculiar property; we say that the risk difference and risk ratio are collapsible. However, noncollapsibility is not unique for the odds ratio; the rate difference and rate ratio are generally noncollapsible as well. This may seem paradoxical, since the rate can be viewed as a risk per unit time, and thus one would naively suspect that the rate difference/ratio should inherit collapsibility from the risk difference/ratio. Adding to the confusion, it was recently shown that the exposure coefficient in the Aalen additive hazards model is collapsible. This may seem to contradict the fact that the rate difference is generally noncollapsible, since the exposure coefficient in the Aalen additive hazards model is a rate difference. In this article, we use graphical arguments to explain why the rate difference/ratio does not inherit collapsibility from the risk difference/ratio. We also explain when and why the exposure coefficient in the Aalen additive hazards model is collapsible.

Argument graphs and assumption-based argumentation

Arguments in structured argumentation are usually defined as trees, and extensions as sets of such tree-based arguments with various properties depending on the particular argumentation semantics. However, these arguments and extensions may have redundancies as well as circularities, which are conceptually and computationally undesirable. Focusing on the specific case of Assumption-Based Argumentation (ABA), we propose novel notions of arguments and admissible/grounded extensions, both defined in terms of graphs. We show that this avoids the redundancies and circularities of standard accounts, and set out the relationship to standard tree-based arguments and admissible/grounded extensions (as sets of arguments). We also define new notions of graph-based admissible/grounded dispute derivations for ABA, for determining whether specific sentences hold under the admissible/grounded semantics. We show that these new derivations are superior with respect to standard dispute derivations in that they are complete in general, rather than solely for restricted classes of ABA frameworks. Finally, we present several experiments comparing the implementation of graph-based admissible/grounded dispute derivations with implementations of standard dispute derivations, suggesting that the graph-based approach is computationally advantageous.

Formalizing Informal Logic

This paper presents a formalization of informal logic using the Carneades Argumentation System (CAS), a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. CAS also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

A complex dynamical approach of Chebyshev’s method

The aim of this paper is to investigate the iterative root-finding Chebyshev’s method from a dynamical perspective. We analyze the behavior of the method applied to low degree polynomials. In this work we focus on the complex case. Actually, we show the existence of extraneous fixed points for Chebyshev’s, that is fixed points of the iterative method that are not roots of the involved polynomial. This fact is a distinguishing feature in the dynamical study of Chebyshev’s method compared with other known iterative methods such as Newton’s or Halley’s methods. In addition, we provide some analytic, geometrical and graphical arguments to explain when and why the method fails, that is, there exists open set of initial points such that the corresponding iterative sequence does not converge to any of the roots.

Two proving strategies of highly successful mathematics majors

We examined the proof-writing behaviors of six highly successful mathematics majors on novel proving tasks in calculus. We found two approaches that these students used to write proofs, which we termed the targeted strategy and the shotgun strategy. When using a targeted strategy students would develop a strong understanding of the statement they were proving, choose a plan based on this understanding, develop a graphical argument for why the statement is true, and formalize this graphical argument into a proof. When using a shotgun strategy, students would begin trying different proof plans immediately after reading the statement and would abandon a plan at the first sign of difficulty. The identification of these two strategies adds to the literature on proving by informing how elements of existing problem-solving models interrelate.

Binomial Sampling Charts Revisited with Graphical and Analytical Arguments

ABSTRACTConfidence interval estimation via binomial sampling charts is an important tool in the reliability field. The topic of reliability can be taught in engineering programmes at both the undergraduate and the graduate levels. It is demonstrated how to apply the binomial distribution-based belt curves to predict confidence intervals. Our demonstrated approach relies on charts that are readily available for typical confidence levels, such as, 80%, 90%, 95%, or 99%. It is the proposition of this paper that understanding the basis for the graphical confidence interval prediction method is significantly easier to appreciate if the formal analysis, which can be found in more advanced texts on reliability, is combined with visual representations for the connections between two distributions: the discrete binomial distribution and continuous partial beta distribution. The paper is presented using a combination of analytical and graphical arguments that leads to the expressions that reproduce the belt curves consistent with the “gold standard” of the Clopper–Pearson (C&P) 1934 model. The detail is sufficient to generate belt curves using a math software package. Examples illustrating the technique for predicting confidence limits with confidence belt curves are included. Students’ assessment data are also provided to support the effectiveness of the combined approach.

Checking termination of bottom-up evaluation of logic programs with function symbols

AbstractRecently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness of models and termination of the evaluation procedure, in the general case, are not guaranteed anymore. Since the program termination problem is undecidable in the general case, several decidable criteria (called program termination criteria) have been recently proposed. However, current conditions are not able to identify even simple programs, whose bottom-up execution always terminates. The paper introduces new decidable criteria for checking termination of logic programs with function symbols under bottom-up evaluation, by deeply analyzing the program structure. First, we analyze the propagation of complex terms among arguments by means of the extended version of the argument graph calledpropagation graph. The resulting criterion, calledacyclicity, generalizes most of the decidable criteria proposed so far. Next, we study how rules may activate each other and define a more powerful criterion, calledsafety. This criterion uses the so-calledsafety functionable to analyze how rules may activate each other and how the presence of some arguments in a rule limits its activation. We also study the application of the proposed criteria to bound queries and show that the safety criterion is well-suited to identify relevant classes of programs and bound queries. Finally, we propose a hierarchy of classes of terminating programs, calledk-safety, where thek-safe class strictly includes the (k-1)-safe class.

Constructing argument graphs with deductive arguments: a tutorial

A deductive argument is a pair where the first item is a set of premises, the second item is a claim, and the premises entail the claim. This can be formalised by assuming a logical language for the premises and the claim, and logical entailment (or

Peirce: A Guide for the Perplexed By Cornelis de Waal

Reviewed by: Peirce: A Guide for the Perplexed by Cornelis de Waal Helmut Pape Cornelis de Waal Peirce: A Guide for the Perplexed London / New York, Bloomsbury, 2013, 183 pp.; index. Introducing the perplexed reader to a philosophy requires both a comprehensive understanding of the philosophy in question and a rigorous simplifying strategy. But clarity and accessibility come at a price: one has to cut down on complicated and perhaps unresolved lines of thought and arguments, stratifying the development of theoretical positions into a coherent and accessible narrative. This review will address both the success of this book as an introduction and, rather unjustly, those more complex topics that have been left out and might be of interest to readers of this journal. First of all, let me say that Cornelis de Waal’s Peirce: A Guide for the Pexplexed is a very good introduction to Peirce’s philosophy. The book opens a road to a more comprehensive understanding of Peirce’s philosophy. The nine chapters of the book, following the opening chapter on “Life and Work” and concluding with the ninth chapter on “Mind, God, and Cosmos,” present Peirce’s philosophy by following, more or less, the final version of Peirce’s classification of the sciences of discovery. The path generated in this way connects systematically the theses, principles and arguments in the different fields of Peirce’s philosophical thought, connecting his view of mathematics as a purely hypothetical discipline with his evolutionary metaphysics and philosophy of religion. In this classification, the place of a science in the sequence depends on its generality, special sciences depending on the more general, comprehensive ones. Or, to put it differently: the more specific the objects of a science, the later it will appear in the systematic sequence. Peirce’s notion of an object plays a special role here. The object is conceived like the causa finalis of a science, functioning as the regulative idea that connects a community of researchers with their field of work. De Waal does not mention this crucial role of the objects of a science and in Chapter 5, which deals with semiotics, he even claims that Peirce’s account of an object and his distinction between an immediate and dynamical object is “fairly traditional.” I will show later on why this claim is misleading and problematic. [End Page 162] But de Waal is right in pointing out that Peirce regards mathematics as a purely hypothetical discipline, because it can be applied to objects of all sorts. In following the descending generality of classification, the second chapter starts with a discussion of “Mathematics and Philosophy.” Here de Waal makes a move that is both fruitful and suggestive. The graphical demonstration (18f) that the sum of the angles of a triangle is equal to the sum of two right angles is used to show that such a proof cannot be a syllogistic one. In this way de Waal achieves several things at the same time. The reader is introduced to Peirce’s visual and mathematical style of thought. The diagrammatic construction of conceptual relations illustrates how Peirce generalizes the Kantian idea that there are necessary conceptual constructions in mathematics that are based on the form of perception. This way of dealing with mathematical principles establishes a crucial difference between Peirce’s and Kant’s thought and exemplifies Peirce’s idea that pure mathematics cannot be a positive science but is a science of hypothetical construction. In this way the ground is prepared for the graphical argument illustrating Peirce’s theorem about the sufficiency of three categories in Chapter 3 on “Phenomenology and the Categories” (41f). Without much ado, de Waal shows in this chapter that Peirce’s phenomenology is a radical undertaking and that the categories are both concrete and general. De Waal models the claim that the three categories are sufficient and irreducible to one another by showing that in a sequence of diagrams, the transformation between three dots and the lines connecting them requires only three categories (42). What I find at once interesting and problematic in de Waal’s guide is the characterization of Peirce’s general philosophical position. By far the majority of scholars now...

How optimal foragers should respond to habitat changes: a reanalysis of the Marginal Value Theorem

The Marginal Value Theorem (MVT) is a cornerstone of biological theory. It connects the quality and distribution of patches in a fragmented habitat to the optimal time an individual should spend exploiting them, and thus its optimal rate of movement. However, predictions regarding how habitat alterations should impact optimal strategies have remained elusive, with heavy reliance on graphical arguments. Here we derive the sensitivity of realized fitness and optimal residence times to general habitat attributes, for homogeneous and heterogeneous habitats, retaining the level of generality of the MVT. We provide new predictions on how altering travel times, patch qualities and/or relative abundances should affect optimal strategies, and study the consequences of habitat heterogeneity. We show that knowledge of average characteristics is in general not sufficient to predict the change in the average rate of movement. We apply our results to examine the conditions under which the optimal strategies are invariant to scaling. We prove a previously conjectured form of invariance in homogeneous habitats, but show that invariances to scaling are not generic in heterogeneous habitats. We also consider the relative exploitation of patches that differ in quality, clarifying the conditions under which it is adaptive to stay longer on poorer patches.

Probabilistic qualification of attack in abstract argumentation

An argument graph is a graph where each node denotes an argument, and each arc denotes an attack by one argument on another. It offers a valuable starting point for theoretical analysis of argumentation following the proposals by Dung. However, the definition of an argument graph does not take into account the belief in the attacks. In particular, when constructing an argument graph from informal arguments, where each argument is described in free text, it is often evident that there is uncertainty about whether some of the attacks hold. This might be because there is some expressed doubt that an attack holds or because there is some imprecision in the language used in the arguments. In this paper, we use the set of spanning subgraphs of an argument graph as a sample space. A spanning subgraph contains all the arguments, and a subset of the attacks, of the argument graph. We assign a probability value to each spanning subgraph such that the sum of the assignments is 1. This means we can reflect the uncertainty over which is the actual subgraph using this probability distribution. Using the probability distribution over subgraphs, we can then determine the probability that a set of arguments is admissible or an extension. We can also obtain the probability of an attack relationship in the original argument graph as a marginal distribution (i.e. it is the sum of the probability assigned to each subgraph containing that attack relationship). We investigate some of the features of this proposal, and we consider the utility of our framework for capturing some practical argumentation scenarios.

Bipolarity in argumentation graphs: Towards a better understanding

Different abstract argumentation frameworks have been used for various applications within multi-agents systems. Among them, bipolar frameworks make use of both attack and support relations between arguments. However, there is no single interpretation of the support, and the handling of bipolarity cannot avoid a deeper analysis of the notion of support.In this paper we consider three recent proposals for specializing the support relation in abstract argumentation: the deductive support, the necessary support and the evidential support. These proposals have been developed independently within different frameworks. We restate these proposals in a common setting, which enables us to undertake a comparative study of the modellings obtained for the three variants of the support. We highlight relationships and differences between these variants, namely a kind of duality between the deductive and the necessary interpretations of the support.

A probabilistic approach to modelling uncertain logical arguments

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.