Argumentation Label Functions - Technical Report

An important approach to abstract argumentation is the labeling-based approach, in which one makes use of labelings that assign to each argument one of three labels: in, out or und. In this paper, we address the question, which of the twenty-seven functions from the set of labels to the set of labels can be represented by an argumentation framework. We prove that in preferred, complete and grounded semantics, eleven labeling functions can be represented in this way while sixteen labeling functions cannot be represented by any argumentation framework. We show how this analysis of labeling functions can be applied to prove an impossibility result: Argumentation frameworks extended with a certain kind of weak attack relation cannot be flattened to the standard Dung argumentation frameworks

Metalogical Contributions to the Nonmonotonic Theory of Abstract Argumentation

The study of nonmonotonic logics is one mayor field of Artificial Intelligence (AI). The reason why such kind of formalisms are so attractive to model human reasoning is that they allow to withdraw former conclusion. At the end of the 1980s the novel idea of using argumentation to model nonmonotonic reasoning emerged in AI. Nowadays argumentation theory is a vibrant research area in AI, covering aspects of knowledge representation, multi-agent systems, and also philosophical questions. Phan Minh Dung’s abstract argumentation frameworks (AFs) play a dominant role in the field of argumentation. In AFs arguments and attacks between them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. Although, Dung-style AFs are among the simplest argumentation systems one can think of, this approach is still powerful. It can be seen as a general theory capturing several nonmonotonic formalisms as well as a tool for solving well-known problems as the stable-marriage problem. This thesis is mainly concerned with the investigation of metalogical properties of Dung’s abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics

On the input/output behavior of argumentation frameworks

This paper tackles the fundamental questions arising when looking at argumentation frameworks as interacting components, characterized by an Input/Output behavior, rather than as isolated monolithical entities. This modeling stance arises naturally in some application contexts, like multi-agent systems, but, more importantly, has a crucial impact on several general application-independent issues, like argumentation dynamics, argument summarization and explanation, incremental computation, and inter-formalism translation. Pursuing this research direction, the paper introduces a general modeling approach and provides a comprehensive set of theoretical results putting the intuitive notion of Input/Output behavior of argumentation frameworks on a solid formal ground. This is achieved by combining three main ingredients. First, several novel notions are introduced at the representation level, notably those of argumentation framework with input, of argumentation multipole, and of replacement of multipoles within a traditional argumentation framework. Second, several relevant features of argumentation semantics are identified and formally characterized. In particular, the canonical local function provides an input-aware semantics characterization and a suite of decomposability properties are introduced, concerning the correspondences between semantics outcomes at global and local level. The third ingredient glues the former ones, as it consists of the investigation of some semantics-dependent properties of the newly introduced entities, namely S-equivalence of multipoles, S-legitimacy and S-safeness of replacements, and transparency of a semantics with respect to replacements. Altogether they provide the basis and draw the limits of sound interchangeability of multipoles within traditional frameworks. The paper develops an extensive analysis of all the concepts listed above, covering seven well-known literature semantics and taking into account various, more or less constrained, ways of partitioning an argumentation framework. Diverse examples, taken from the literature, are used to illustrate the application of the results obtained and, finally, an extensive discussion of the related literature is provided

Syntactic reconstruction in Indo-European : the state of the art

Interest in syntactic reconstruction was implicit in the work of the founding fathers of the Comparative Method, including Franz Bopp and his contemporaries. The Neo-Grammarians took a more active interest in syntactic issues, concentrating especially on comparative descriptive syntax. In the 20th century, typologically-inspired research gave rise to several reconstructions of neutral word order for Proto-Indo-European. This work was met with severe criticism by Watkins (1976), which had the unfortunate effect that work on syntactic reconstruction reached a methodological impasse and was largely abandoned. However, the pioneering work of Hale (1987a), Garrett (1990) and Harris & Campbell (1995) showed that syntactic reconstruction could be carried out successfully. Currently, three different strands of work on syntactic reconstruction can be identified: i) the traditional Indo-Europeanists, ii) the generativists, and iii) the construction grammarians. The reconstructions of the two first strands are incomplete, either due to lack of formal representation, or due to the inability of the representational system to explicate the details of the form-meaning correspondences underlying any analysis of syntactic reconstruction. In contrast, Construction Grammar has at its disposal a full-fledged representational formalism where all aspects of grammar can be made explicit, hence allowing for the precise formulations of form-meaning correspondences needed to carry out a complete reconstruction. This is exemplified in the present paper with a reconstruction of grammatical relations for Proto-Germanic, involving a set of argument structure constructions and the subject tests applicable in the grammar of the proto-stage

Question/answer congruence and the semantics of wh-phrases

This paper is about the semantics of wh-phrases. It is argued that wh-phrases should not be analyzed as indefinites as, for example, Karttunen (1977) and many others have done, but as functional expressions with an indefinite core -their function being to restrict possible focus/background structures in direct or congruent answers. This will be argued for on the basis of observations made with respect to the distribution of term answers in well-formed question/answer sequences. This claim having been established, it will be integrated in a categorial variant of Schwarzschild's (1999) information-theoretic approach to F-marking and accent placement, and – second – its consequences with respect to the focus/background structure of wh-questions will be outlined

Labeled bipolar argumentation frameworks

An essential part of argumentation-based reasoning is to identify arguments in favor and against a statement or query, select the acceptable ones, and then determine whether or not the original statement should be accepted. We present here an abstract framework that considers two independent forms of argument interaction-support and conflict-and is able to represent distinctive information associated with these arguments. This information can enable additional actions such as: (i) a more in-depth analysis of the relations between the arguments; (ii) a representation of the user's posture to help in focusing the argumentative process, optimizing the values of attributes associated with certain arguments; and (iii) an enhancement of the semantics taking advantage of the availability of richer information about argument acceptability. Thus, the classical semantic definitions are enhanced by analyzing a set of postulates they satisfy. Finally, a polynomial-time algorithm to perform the labeling process is introduced, in which the argument interactions are considered.Fil: Escañuela Gonzalez, Melisa Gisselle. Universidad Nacional de Santiago del Estero; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán; ArgentinaFil: Budan, Maximiliano Celmo David. Universidad Nacional de Santiago del Estero; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán; ArgentinaFil: Simari, Gerardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin

How grammar introduces asymmetry into cognitive structures: compositional semantics, metaphors, and schematological hybrids

This paper presents a preliminary and tentative formulation of a novel empirical generalization governing the relationship between grammar and cognition across a variety of independent domains. Its point of departure is an abstract distinction between two kinds of cognitive structures: symmetric and asymmetric. While in principle any feature whatsoever has the potential for introducing asymmetry, this paper focuses on one specific feature, namely thematic-role assignment. Our main empirical finding concerns the role of language, or, more specifically, grammar, in effecting and maintaining the distinction between symmetric and asymmetric cognitive structures. Specifically, whereas symmetric structures devoid of thematic-role assignment more commonly occur in a non-grammatical and usually also non-verbal medium, asymmetric structures involving thematic-role assignment are more likely to be associated with a grammatical medium. Our work draws together three independent strands of empirical research associated with three diverse phenomenological domains: compositional semantics, metaphors and schematological hybrids. These three domains instantiate conceptual combinations, bringing together two or more subordinate entities into a single superordinate entity. For compositional semantics this consists of a juxtaposition of constituent signs to form a single more complex sign; for metaphors this entails the bringing together of two different concepts in order to produce a comparison; while for schematological hybrids this involves the combination of different entities to form a single new hybrid entity. Our empirical results reveal a remarkable parallelism between the above three domains. Within each domain, symmetric structures tend to be associated with a non-verbal or otherwise non-grammatical medium, while asymmetric structures are more frequently associated with a grammatical medium. Thus, within each domain, grammar introduces asymmetry. More specifically, we find that in all three domains, the asymmetry in question is one that involves the assignment of thematic roles. To capture this effect, we posit two distinct levels, or tiers, of cognition: non-grammatical cognition, more commonly associated with symmetric structures, and grammatical cognition more conducive to asymmetric structures. Within each of the three phenomenological domains, we find the distinction between non-grammatical and grammatical cognition to be manifest in three independent realms, phylogeny, ontogeny, and the architecture of human cognition. Thus, grammar constitutes the driving force behind the transition from symmetric to asymmetric cognitive structures.Introduction Thematic Role Assignment Compositional Semantics Metaphors Schematological Hybrids Conclusio

Argumentation as Exogenous Coordination

Formal argumentation is one of the most popular approaches in modern logic and reasoning. The theory of abstract argumentation introduced by Dung in 1995 has shifted the focus from the internal structure of arguments to relations among arguments, and temporal dynamics for abstract argumentation was proposed by Barringer, Gabbay and Woods in 2005. In this tradition, we see arguments as reasoning processes, and the interaction among them as a coordination process.We argue that abstract argumentation can adopt ideas and techniques from formal theories of coordination, and as an example we propose a model of sequential abstract argumentation loosely inspired by Reo’s model of exogenous coordination. We show how the argumentation model can represent the temporal dynamics of the liar paradox and predator-prey like behaviour