Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming

In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3-valued stable models in logic programming. This result is in line with earlier work of [6] that identified the correspondence between the grounded extension in abstract argumentation and the well-founded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming.     

Meta-Argumentation Modelling I: Methodology and Techniques

In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s abstract arguments with meta-arguments using a technique called flattening. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages.     

Modal Logics of Reactive Frames

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques.     

Logical Modes of Attack in Argumentation Networks

This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent.     

Annotation Theories over Finite Graphs

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21].     

Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix \({\mathbb {A}}\) with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a _i,j =?. The method allows us to decide whether to declare a _i,j = 0 or a _i,j = 1 or a _i,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences.     

Loyalty and Creativity in a Disciplinary Organization

The relationship between loyalty to rules and the creativity that attempts to improve those same rules was examined among Norwegian army officers deployed in international operations. Today's army officers are faced with rapidly changing work conditions and unpredictable enemies, both of which challenge and outdate rules and routines. They thus may experience that they are either guided by too few or inadequate rules, or by many rules that need to be constantly updated. Assuming that following rules is advantageous to officers, then, contrary to classical theory, it was hypothesized that officers scoring both low and high on loyalty to rules would score high on creativity. Hierarchical regression analyses revealed a significant U‐shaped relationship between loyalty to rules and creativity.     

Predicting school adjustment from motor abilities in kindergarten

The present study assessed the relations between basic motor abilities in kindergarten and scholastic, social, and emotional adaptation in the transition to formal schooling. Seventy‐one five‐year‐old kindergarten children were administered a battery of standard assessments of basic motor functions. A year later, children's adjustment to school was assessed via a series of questionnaires completed by the children and their class teachers. The results indicate that in addition to the already documented association between visual–motor integration and academic achievement, other motor functions show significant predictive value to both scholastic adaptation and social and emotional adjustment to school. The results further suggest a better prediction of scholastic adaptation and level of disruptive behaviour in school when using an aggregate measure of children's ability in various motor domains than when using assessments of singular motor functions. It is concluded that good motor ability may serve as a buffer to the normative challenges presented to children in the transition to school. In contrast, poor motor ability emerges as a vulnerability factor in the transition to formal schooling. Copyright © 2007 John Wiley & Sons, Ltd.