Matthias Thimm

A probabilistic semantics for abstract argumentation

Classical semantics for abstract argumentation frameworks are usually defined in terms of extensions or, more recently, labelings. That is, an argument is either regarded as accepted with respect to a labeling or not. In order to reason with a specific semantics one takes either a credulous or skeptical approach, i. e. an argument is ultimately accepted, if it is accepted in one or all labelings, respectively. In this paper, we propose a more general approach for a semantics that allows for a more fine-grained differentiation between those two extreme views on reasoning. In particular, we propose a probabilistic semantics for abstract argumentation that assigns probabilities or degrees of belief to individual arguments. We show that our semantics generalizes the classical notions of semantics and we point out interesting relationships between concepts from argumentation and probabilistic reasoning. We illustrate the usefulness of our semantics on an example from the medical domain.

Inconsistency measures for probabilistic logics

Inconsistencies in knowledge bases are of major concern in knowledge representation and reasoning. In formalisms that employ model-based reasoning mechanisms inconsistencies render a knowledge base useless due to the non-existence of a model. In order to restore consistency an analysis and understanding of inconsistencies are mandatory. Recently, the field of inconsistency measurement has gained some attention for knowledge representation formalisms based on classical logic. An inconsistency measure is a tool that helps the knowledge engineer in obtaining insights into inconsistencies by assessing their severity. In this paper, we investigate inconsistency measurement in probabilistic conditional logic, a logic that incorporates uncertainty and focuses on the role of conditionals, i.e. if-then rules. We do so by extending inconsistency measures for classical logic to the probabilistic setting. Further, we propose novel inconsistency measures that are specifically tailored for the probabilistic case. These novel measures use distance measures to assess the distance of a knowledge base to a consistent one and therefore takes the crucial role of probabilities into account. We analyze the properties of the discussed measures and compare them using a series of rationality postulates.

SPLODGE: systematic generation of SPARQL benchmark queries for linked open data

The distributed and heterogeneous nature of Linked Open Data requires flexible and federated techniques for query evaluation. In order to evaluate current federation querying approaches a general methodology for conducting benchmarks is mandatory. In this paper, we present a classification methodology for federated SPARQL queries. This methodology can be used by developers of federated querying approaches to compose a set of test benchmarks that cover diverse characteristics of different queries and allows for comparability. We further develop a heuristic called SPLODGE for automatic generation of benchmark queries that is based on this methodology and takes into account the number of sources to be queried and several complexity parameters. We evaluate the adequacy of our methodology and the query generation strategy by applying them on the 2011 billion triple challenge data set.

Summary Report of The First International Competition on Computational Models of Argumentation

We review the First International Competition on Computational Models of Argumentation (ICMMA’15). The competition evaluated submitted solvers performance on four different computational tasks related to solving abstract argumentation frameworks. Each task evaluated solvers in ways that pushed the edge of existing performance by introducing new challenges. Despite being the first competition in this area, the high number of competitors entered, and differences in results, suggest that the competition will help shape the landscape of ongoing developments in argumentation theory solvers.

Strategic Argumentation in Multi-Agent Systems

Argumentation-based negotiation describes the process of decision-making in multi-agent systems through the exchange of arguments. If agents only have partial knowledge about the subject of a dialogue strategic argumentation can be used to exploit weaknesses in the argumentation of other agents and thus to persuade other agents of a specific opinion and reach a certain outcome. This paper gives an overview of the field of strategic argumentation and surveys recent works and developments. We provide a general discussion of the problem of strategic argumentation in multi-agent settings and discuss approaches to strategic argumentation, in particular strategies based on opponent models.

Probabilistic argumentation with incomplete information

We consider augmenting abstract argumentation frameworks with probabilistic information and discuss different constraints to obtain meaningful probabilistic information. Moreover, we investigate the problem of incomplete probability assignments and propose a solution for completing these assignments by applying the principle of maximum entropy.

Relational probabilistic conditional reasoning at maximum entropy

This paper presents and compares approaches for reasoning with relational probabilistic conditionals, i. e. probabilistic conditionals in a restricted first-order environment. It is well-known that conditionals play a crucial role for default reasoning, however, most formalisms are based on propositional conditionals, which restricts their expressivity. The formalisms discussed in this paper are relational extensions of a propositional conditional logic based on the principle of maximum entropy. We show how this powerful principle can be used in different ways to realize model-based inference relations for first-order probabilistic knowledge bases. We illustrate and compare the different approaches by applying them to several benchmark examples, and we evaluate each approach with respect to properties adopted from default reasoning. We also compare our approach to Bayesian logic programs (BLPs) from the field of statistical relational learning which focuses on the combination of probabilistic reasoning and relational knowledge representation as well.

Realizing argumentation in multi-agent systems using defeasible logic programming

We describe a working multi-agent architecture based on Defeasible Logic Programming (DeLP) where agents are engaged in an argumentation to reach a common conclusion. Due to the distributed approach personalities and opinions of the individual agents give rise to arguments and counterarguments concerning a particular query. This distribution of information leads to more intuitive modeling of argumentation from the point of view of knowledge representation. We establish a sound theoretical framework of a specific type of argumentation in multi-agent systems and describe the computational issues involved in it. A formal comparison of the framework to DeLP is given and it is shown that the modeling specific scenarios of argumentation in the distributed setting bears a more rational representation. The framework described in this paper has been fully implemented and a short description of its features is given.

Consolidation of probabilistic knowledge bases by inconsistency minimization

Consolidation describes the operation of restoring consistency in an inconsistent knowledge base. Here we consider this problem in the context of probabilistic conditional logic, a language that focuses on probabilistic conditionals (if-then rules). If a knowledge base, i. e., a set of probabilistic conditionals, is inconsistent traditional model-based inference techniques are not applicable. In this paper, we develop an approach to repair such knowledge bases that relies on a generalized notion of a model of a knowledge base that extends to classically inconsistent knowledge bases. We define a generalized approach to reasoning under maximum entropy on these generalized models and use it to repair the knowledge base. This approach is founded on previous work on inconsistency measures and we show that it is well-defined, provides a unique solution, and satisfies other desirable properties.

Stream-based inconsistency measurement

Inconsistency measures have been proposed to assess the severity of inconsistencies in knowledge bases of classical logic in a quantitative way. In general, computing the value of inconsistency is a computationally hard task as it is based on the satisfiability problem which is itself NP-complete. In this work, we address the problem of measuring inconsistency in knowledge bases that are accessed in a stream of propositional formulae. That is, the formulae of a knowledge base cannot be accessed directly but only once through processing of the stream. This work is a first step towards practicable inconsistency measurement for applications such as Linked Open Data, where huge amounts of information is distributed across the web and a direct assessment of the quality or inconsistency of this information is infeasible due to its size. Here we discuss the problem of stream-based inconsistency measurement on classical logic, in order to make use of existing measures for classical logic. However, it turns out that inconsistency measures defined on the notion of minimal inconsistent subsets are usually not apt to be used in the streaming scenario. In order to address this issue, we adapt measures defined on paraconsistent logics and also present a novel inconsistency measure based on the notion of a hitting set. We conduct an extensive empirical analysis on the behavior of these different inconsistency measures in the streaming scenario, in terms of runtime, accuracy, and scalability. We conclude that for two of these measures, the stream-based variant of the new inconsistency measure and the stream-based variant of the contension inconsistency measure, large-scale inconsistency measurement in streaming scenarios is feasible. We present a novel inconsistency measure based on hitting sets and show how this measure relates to other measures.We formalize a theory of inconsistency measurement in streams and relate it to the classical setting of inconsistency measurement.We provide a methodology for applying inconsistency measures to the streaming case and also develop novel approaches.We conduct an extensive empirical study on those inconsistency measures in terms of runtime, accuracy, and scalability.