Probabilistic Reasoning with Abstract Argumentation Frameworks

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by considering probability assignments on arguments, allowing for a quantitative treatment of formal argumentation. In this paper, we regard the assignment as denoting the degree of belief that an agent has in an argument being acceptable. While there are various interpretations of this, an example is how it could be applied to a deductive argument. Here, the degree of belief that an agent has in an argument being acceptable is a combination of the degree to which it believes the premises, the claim, and the derivation of the claim from the premises. We consider constraints on these probability assignments, inspired by crisp notions from classical abstract argumentation frameworks and discuss the issue of probabilistic reasoning with abstract argumentation frameworks. Moreover, we consider the scenario when assessments on the probabilities of a subset of the arguments are given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalise this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistency-tolerant reasoning

Topical Results on Lattice Chiral Fermions in the CFA

We report new results on the lattice regularization of the chiral Schwinger model and the chiral U(1) model in four dimensions in the CFA.Comment: LATTICE98(chiral

On the eta-invariant in the four dimensional chiral U(1) theory

The imaginary part of the effective action is investigated in the 4D chiral U(1) theory using the CFA.Comment: LATTICE99(Chiral Gauge Theories), typo fixe

Towards Large-scale Inconsistency Measurement

We investigate the problem of inconsistency measurement on large knowledge bases by considering stream-based inconsistency measurement, i.e., we investigate inconsistency measures that cannot consider a knowledge base as a whole but process it within a stream. For that, we present, first, a novel inconsistency measure that is apt to be applied to the streaming case and, second, stream-based approximations for the new and some existing inconsistency measures. We conduct an extensive empirical analysis on the behavior of these inconsistency measures on large knowledge bases, in terms of runtime, accuracy, and scalability. We conclude that for two of these measures, the approximation of the new inconsistency measure and an approximation of the contension inconsistency measure, large-scale inconsistency measurement is feasible.Comment: International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), co-located with the 21st European Conference on Artificial Intelligence (ECAI 2014). Proceedings of the International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), pages 63-70, technical report, ISSN 1430-3701, Leipzig University, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-15056

Lattice Chiral Schwinger Model in the Continuum Formulation

We pursue further an approach to lattice chiral fermions in which the fermions are treated in the continuum. To render the effective action gauge invariant, counterterms have to be introduced. We determine the counterterms for smooth gauge fields, both analytically and numerically. The final result is that the imaginary part of the effective action can be computed analytically from the lattice gauge field, while the real part is given by one half of the action of the corresponding vector model.Comment: 3 pages, 2 figures, contribution to the LATTICE97 Proceeding

Many-body theory of the quantum mirage

In recent scanning tunneling microscopy experiments, confinement in an elliptical corral has been used to project the Kondo effect from one focus to the other one. I solve the Anderson model at arbitrary temperatures, for an impurity hybridized with eigenstates of an elliptical corral, each of which has a resonant level width delta. This width is crucial. If delta < 20 meV, the Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For particular conditions, a stronger mirage with the impurity out of the foci is predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a reference included to show that the hybridization of the impurity with bulk states can be neglecte

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 re- flecting 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

Lattice chiral fermions in the background of non-trivial topology

We address the problem of numerical simulations in the background non-trivial topology in the chiral Schwinger model. An effective fermionic action is derived which is in accord with established analytical results, and which satisfies the anomaly equation. We describe a numerical evaluation of baryon number violating amplitudes, specifically the 't Hooft vertex.Comment: LATTICE99(Chiral Gauge Theories

Kann Lateinamerika von der Globalisierung des Kapitals profitieren?

"Die Kapitalströme, die rund um den Globus bewegt werden, haben sich während der zurückliegenden Jahre verdreifacht. An den internationalen Finanzmärkten steht Lateinamerikas Volkswirtschaften reichlich privates Kapital zur Finanzierung ihrer Entwicklung zur Verfügung. Aber auch öffentliche Entwicklungsbanken haben weiterhin eine wichtige Funktion zu erfüllen. Die Globalisierung des Kapitals eröffnet Chancen, birgt allerdings auch Risiken. Bevorzugt fließt privates Auslandskapital in diejenigen Länder Lateinamerikas, deren dynamische Märkte Wachstumschancen und Profitabilität verheißen, die ihre Finanz- und Kapitalmärkte liberalisiert haben und in denen gesamtwirtschaftliche Stabilität den Kapitalanlegern relative Sicherheit verspricht. Der Nettozufluss ausländischen Kapitals nach Lateinamerika hat sich in den zurückliegenden fünf Jahren deutlich vermindert. Öffentliche Finanzmittel und kommerzielle Bankkredite sind für die meisten Volkswirtschaften der Region nur noch von nachrangiger Bedeutung. Ausländische Direktinvestitionen sind für Lateinamerika zur wichtigsten externen Finanzierungsquelle geworden. Die nationalen und regionalen öffentlichen Entwicklungsbanken müssen sich den neuen Gegebenheiten anpassen und neuen Herausforderungen stellen; dies umfasst insbesondere eine Differenzierung und Profilierung der jeweiligen Kreditvergabepolitik - auch gegenüber der neuen Banco del Sur." (Autorenreferat