We present machine-learning-based approaches for determining the \emph{degree} of inconsistency -- which is a numerical value -- for propositional logic knowledge bases. Specifically, we present regression- and neural-based models that learn to predict the values that the inconsistency measures $\incmi$ and $\incat$ would assign to propositional logic knowledge bases. Our main motivation is that computing these values conventionally can be hard complexity-wise. As an important addition, we use specific postulates, that is, properties, of the underlying inconsistency measures to infer symbolic rules, which we combine with the learning-based models in the form of constraints. We perform various experiments and show that a) predicting the degree values is feasible in many situations, and b) including the symbolic constraints deduced from the rationality postulates increases the prediction quality.

This volume contains revised versions of the papers selected for the fourth volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

This paper presents Tweety, an open source project for scientific experimentation on logical aspects of artificial intelligence and particularly knowledge representation. Tweety provides a general framework for implementing and testing knowledge representation formalisms in a way that is familiar to researchers used to logical formalizations. This framework is very general, widely applicable, and can be used to implement a variety of knowledge representation formalisms from classical logics, over logic programming and computational models for argumentation, to probabilistic modeling approaches. Tweety already contains over 15 different knowledge representation formalisms and allows easy computation of examples, comparison of algorithms and approaches, and benchmark tests. This paper gives an overview on the technical architecture of Tweety and a description of its different libraries. We also provide two case studies that show how Tweety can be used for empirical evaluation of different problems in artificial intelligence.

We address the issue of quantitatively assessing the severity of inconsistencies in nonmonotonic frameworks. While measuring inconsistency in classical logics has been investigated for some time now, taking the nonmonotonicity into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly kb-inconsistent subsets of a knowledge base kb---a generalization of minimal inconsistency to arbitrary, possibly nonmonotonic, frameworks. We propose measures based on this notion and investigate their behavior in a nonmonotonic setting by revisiting existing rationality postulates, analyzing the compliance of the proposed measures with these postulates, and by investigating their computational complexity.

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.

The classical probabilistic entailment problem is to We apply the family of minimal violation measures from determine upper and lower bounds on the probability [Potyka, 2014] since they allow us to extend the classical notion of formulas, given a consistent set of probabilistic of models of a probabilistic knowledge base to inconsistent assertions. We generalize this problem ones. Intuitively, the generalized models are those probability by omitting the consistency assumption and, thus, functions that minimally violate the knowledge base provide a general framework for probabilistic reasoning [Potyka and Thimm, 2014]. We incorporate integrity constraints under inconsistency. To do so, we utilize and study a family of generalized entailment problems inconsistency measures to determine probability for probabilistic knowledge bases. More specifically, functions that are closest to satisfying the knowledge the contributions of this work are as follows: base. We illustrate our approach on several 1. We introduce the computational problem of generalized examples and show that it has both nice formal and entailment with integrity constraints in probabilistic logics computational properties.

Computational models of argument could play a valuable role in persuasion technologies for behaviour change (e.g. persuading a user to eat a more healthy diet, or to drink less, or to take more exercise, or to study more conscientiously, etc). For this, the system (the persuader) could present arguments to convince the user (the persuadee). In this paper, we consider asymmetric dialogues where only the system presents arguments, and the system maintains a model of the user to determine the best choice of arguments to present (including counterarguments to key arguments believed to be held by the user). The focus of the paper is on the user model, including how we update it as the dialogue progresses, and how we use it to make optimal choices for dialogue moves.