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

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

Use marketing strategy in the intrnet space

This article deals with the theory and practice of modern methods of promotion products by industrial. The features of the concept of marketing in the Internet space and theiradvantages

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

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

Epistemic attack semantics

We present a probabilistic interpretation of the plausibility of attacks in abstract argumentation frameworks by extending the epistemic approach to probabilistic argumentation with probabilities on attacks. By doing so we also generalise the previously proposed attack semantics by Villata et al. to the probabilistic setting and provide a fine-grained assessment of the plausibility of attacks. We also consider the setting where partial probabilistic information on arguments and/or attacks is given and missing probabilities have to be derived

A Keck Survey of Gravitational Lens Systems: I. Spectroscopy of SBS 0909+532, HST 1411+5211, and CLASS B2319+051

We present new results from a continuing Keck program to study gravitational lens systems. We have obtained redshifts for three lens systems, SBS 0909+532, HST 1411+5211, and CLASS B2319+051. For all of these systems, either the source or lens redshift (or both) has been previously unidentified. We find (z_l, z_s) = (0.830, 1.377) for SBS 0909+532; (z_l, z_s) = (0.465, 2.811) for HST 1411+5211, although the source redshift is still tentative; and (z_l1, z_l2) = (0.624, 0.588) for the two lensing galaxies in CLASS B2319+051. The background radio source in B2319+051 has not been detected optically; its redshift is, therefore, still unknown. We find that the spectral features of the central lensing galaxy in all three systems are typical of an early-type galaxy. The observed image splittings in SBS 0909+532 and HST 1411+5211 imply that the masses within the Einstein ring radii of the lensing galaxies are 1.4 x 10^{11} and 2.0 x 10^{11} h^{-1} M_sun, respectively. The resulting B band mass-to-light ratio for HST 1411+5211 is 41.3 +/- 1.2 h (M/L)_sun, a factor of 5 times higher than the average early-type lensing galaxy. This large mass-to-light is almost certainly the result of the additional mass contribution from the cluster CL 3C295 at z = 0.46. For the lensing galaxy in SBS 0909+532, we measure (M/L)_B = 4^{+11}_{-3} h (M/L)_sun where the large errors are the result of significant uncertainty in the galaxy luminosity. While we cannot measure directly the mass-to-light ratio of the lensing galaxy in B2319+051, we estimate that (M/L)_B is between 3-7 h (M/L)_sun.Comment: Accepted for publication in Astronomical Journal. 21 pages, including 7 figure

Belief in attacks in epistemic probabilistic argumentation

The epistemic approach to probabilistic argumentation assigns belief to arguments. This is valuable in dialogical argumentation where one agent can model the beliefs another agent has in the arguments and this can be harnessed to make strategic choices of arguments to present. In this paper, we extend this epistemic approach by also representing the belief in attacks. We investigate properties of this proposal and compare it to the constellations approach showing neither subsumes the other