Matthias Thimm

Carl Corea, John Grant, Matthias Thimm

We address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic on fixed traces (LTLff). As we will show, existing inconsistency measures for classical logic cannot provide a meaningful assessment of inconsistency in LTL in general, as they cannot adequately handle the temporal operators. We therefore propose a novel paraconsistent semantics as a framework for inconsistency measurement. We then present two new inconsistency measures based on these semantics and show that they satisfy important desirable properties. We show how these measures can be applied to declarative process models and investigate the computational complexity of the introduced approach.

Matthias Thimm

We revisit the notion of initial sets by Xu and Cayrol, i.e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to explain why certain arguments can be accepted. We contribute with new insights on the structure of initial sets and devise a simple non-deterministic construction principle for any admissible set, based on iterative selection of initial sets of the original framework and its induced reducts. In particular, we characterise many existing admissibility-based semantics via this construction principle, thus providing a constructive explanation on the structure of extensions. We also investigate certain problems related to initial sets with respect to their computational complexity.

Isabelle Kuhlmann, Anna Gessler, Vivien Laszlo et al.

We present algorithms based on satisfiability problem (SAT) solving, as well as answer set programming (ASP), for solving the problem of determining inconsistency degrees in propositional knowledge bases. We consider six different inconsistency measures whose respective decision problems lie on the first level of the polynomial hierarchy. Namely, these are the contension inconsistency measure, the forgetting-based inconsistency measure, the hitting set inconsistency measure, the max-distance inconsistency measure, the sum-distance inconsistency measure, and the hit-distance inconsistency measure. In an extensive experimental analysis, we compare the SAT-based and ASP-based approaches with each other, as well as with a set of naive baseline algorithms. Our results demonstrate that overall, both the SAT-based and the ASP-based approaches clearly outperform the naive baseline methods in terms of runtime. The results further show that the proposed ASP-based approaches perform superior to the SAT-based ones with regard to all six inconsistency measures considered in this work. Moreover, we conduct additional experiments to explain the aforementioned results in greater detail.

Lydia Blümel, Kai Sauerwald, Kenneth Skiba et al.

We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two vertices in a graph, the number of walks of each length ending in those vertices is the same. We employ results from automata theory and reduce this problem to the equivalence problem for semiring automata. This offers a new perspective on the computational complexity of ranking semantics, an area in which the complexity of many semantics remains open.

Lydia Blümel, Matthias Thimm

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics σ and τ, refines σ (base condition) by accepting only those σ-extensions that have no non-empty τ-extension in their reduct (vacuity condition). We give a systematic overview on vacuous reduct semantics resulting from combining different admissibility-based and conflict-free semantics and present a principle-based analysis of vacuous reduct semantics in general. We provide criteria for the inheritance of principle satisfaction by a vacuous reduct semantics from its base and vacuity condition for established as well as recently introduced principles in the context of weak argumentation semantics. We also conduct a principle-based analysis for the special case of undisputed semantics.

Kai Sauerwald, Matthias Thimm

This paper studies the realizability of belief revision and belief contraction operators in epistemic spaces. We observe that AGM revision and AGM contraction operators for epistemic spaces are only realizable in precisely determined epistemic spaces. We define the class of linear change operators, a special kind of maxichoice operator. When AGM revision, respectively, AGM contraction, is realizable, linear change operators are a canonical realization.

Matthias Thimm, Jandson Santos Ribeiro Santos

We analyse a specific instance of the general approach of reasoning based on forgetting by Lang and Marquis. More precisely, we discuss an approach for reasoning with inconsistent information using maximal consistent subsignatures, where a maximal consistent subsignature is a maximal set of propositions such that forgetting the remaining propositions restores consistency. We analyse maximal consistent subsignatures and the corresponding minimal inconsistent subsignatures in-depth and show, among others, that the hitting set duality applies for them as well. We further analyse inference relations based on maximal consistent subsignatures wrt. rationality postulates from non-monotonic reasoning and computational complexity. We also consider the relationship of our approach with inconsistency measurement and paraconsistent reasoning.

Kenneth Skiba, Tjitze Rienstra, Matthias Thimm et al.

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is "closer" to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extension-ranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics. We also adapt a number of approaches from the literature for ranking extensions to be usable in the context of extension-ranking semantics, and evaluate their behaviour.

Matthias Thimm, Federico Cerutti, Mauro Vallati

We present Fudge, an abstract argumentation solver that tightly integrates satisfiability solving technology to solve a series of abstract argumentation problems. While most of the encodings used by Fudge derive from standard translation approaches, Fudge makes use of completely novel encodings to solve the skeptical reasoning problem wrt. preferred semantics and problems wrt. ideal semantics.

Carl Corea, Matthias Thimm, Patrick Delfmann

In this report, we investigate (element-based) inconsistency measures for multisets of business rule bases. Currently, related works allow to assess individual rule bases, however, as companies might encounter thousands of such instances daily, studying not only individual rule bases separately, but rather also their interrelations becomes necessary, especially in regard to determining suitable re-modelling strategies. We therefore present an approach to induce multiset-measures from arbitrary (traditional) inconsistency measures, propose new rationality postulates for a multiset use-case, and investigate the complexity of various aspects regarding multi-rule base inconsistency measurement.

Kenneth Skiba, Matthias Thimm

We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic inference systems to generate a ranking on possible worlds. With this ranking we construct a ranking for our arguments. With a small extension to this ranking-based semantics we already satisfy some desirable properties for a ranking over arguments.

Carl Corea, Matthias Thimm

We investigate the application of inconsistency measures to the problem of analysing business rule bases. Due to some intricacies of the domain of business rule bases, a straightforward application is not feasible. We therefore develop some new rationality postulates for this setting as well as adapt and modify existing inconsistency measures. We further adapt the notion of inconsistency values (or culpability measures) for this setting and give a comprehensive feasibility study.

Anthony Hunter, Sylwia Polberg, Matthias Thimm

This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained alternative to the standard Dung's approaches when it comes to determining the status of a given argument. Furthermore, the flexibility of the epistemic approach allows us to both model the rationale behind the existing semantics as well as completely deviate from them when required. Epistemic graphs can model both attack and support as well as relations that are neither support nor attack. The way other arguments influence a given argument is expressed by the epistemic constraints that can restrict the belief we have in an argument with a varying degree of specificity. The fact that we can specify the rules under which arguments should be evaluated and we can include constraints between unrelated arguments permits the framework to be more context--sensitive. It also allows for better modelling of imperfect agents, which can be important in multi--agent applications.

Sarah A. Gaggl, Matthias Thimm

This volume contains the thesis abstracts presented at the Second Summer School on Argumentation: Computational and Linguistic Perspectives (SSA'2016) held on September 8-12 in Potsdam, Germany.

Matthias Thimm, Serena Villata

This volume contains the system description of the 18 solvers submitted to the First International Competition on Computational Models of Argumentation (ICCMA'15) and therefore gives an overview on state-of-the-art of computational approaches to abstract argumentation problems. Further information on the results of the competition and the performance of the individual solvers can be found on at http://argumentationcompetition.org/2015/.

Matthias Thimm

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.

Anthony Hunter, Matthias Thimm

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed to this assignment. In this paper, we regard the assignment as denoting the belief that an agent has that an argument is justifiable, i.e., that both the premises of the argument and the derivation of the claim of the argument from its premises are valid. This leads to the notion of an epistemic extension which is the subset of the arguments in the graph that are believed to some degree (which we defined as the arguments that have a probability assignment greater than 0.5). We consider various constraints on the probability assignment. Some constraints correspond to standard notions of extensions, such as grounded or stable extensions, and some constraints give us new kinds of extensions.

Matthias Thimm, Gabriele Kern-Isberner

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions.

Matthias Thimm

This paper develops an inconsistency measure on conditional probabilistic knowledge bases. The measure is based on fundamental principles for inconsistency measures and thus provides a solid theoretical framework for the treatment of inconsistencies in probabilistic expert systems. We illustrate its usefulness and immediate application on several examples and present some formal results. Building on this measure we use the Shapley value-a well-known solution for coalition games-to define a sophisticated indicator that is not only able to measure inconsistencies but to reveal the causes of inconsistencies in the knowledge base. Altogether these tools guide the knowledge engineer in his aim to restore consistency and therefore enable him to build a consistent and usable knowledge base that can be employed in probabilistic expert systems.