Matthias Thimm

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• Professor
• Professor (Full) at University of Hagen

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, t...

Conditionals, i. e. expressions of the logical form "if A, then B", have been a central topic of study ever since logic was on the academic menu. In contemporary logic, there is a consensus that the semantics of conditionals are best obtained by stipulating a subset of possible worlds in which the antecedent is true, and verifying whether the conse...

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 re...

We propose two soft notions of the notion of admissibility in abstract argumentation. The first one weakens the defence notion by allowing, to a certain degree, undefended attacks , and the second one allows, to a certain degree, conflicts within sets of arguments. We analyse these new semantical notions based on the computational complexity of opt...

This paper introduces four novel inconsistency-tolerant inference relations for knowledge bases. These relations are based on the minimal hitting sets of a knowledge base, which are sets of interpretations that contains a model of every formula in the knowledge base. We prove several useful properties of hitting sets and the inference relations bas...

We introduce the notion of serialisation equivalence, which provides a notion of equivalence that takes the underlying dialectical structure of extensions in an argumentation framework into account. Under this notion, two argumentation frameworks are considered equivalent if they possess not only the same extensions wrt. some semantics but also the...

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 resul...

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 propositio...

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions that have no non-empty {\tau}-extension in their reduct (vacuity condition). We give a systematic overview on...

We analyse two soft notions of stable extensions in abstract argumentation, one that weakens the requirement of having full range and one that weakens the requirement of conflict-freeness. We then consider optimisation problems over these two notions that represent optimisation variants of the credulous reasoning problem with stable semantics. We i...

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 re...

We introduce an argumentation-based approach for conducting probabilistic causal reasoning. For that, we consider Pearl's causal models where causal relations are modelled via structural equations and a probability distribution over background atoms. The probability that some causal statement holds is then computed by constructing a prob-abilistic...

We present a general framework to rank assumption in assumption based argumentation frameworks (ABA frameworks), relying on their relationship to other assumptions and the syntactical structure of the ABA framework. We propose a new family of semantics for ABA frameworks that is using reductions to the abstract argumentation setting and leveraging...

We present a multi-step classification approach that combines classical machine learning methods with computational models for argumentation. In the first step, the dataset is divided into different groups using a clustering algorithm. In the second step, we employ rule-learning algorithms to extract frequent patterns and rules from each resulting...

Abstract argumentation frameworks model arguments and their relationships as directed graphs, often with the goal of identifying sets of arguments capable of defending themselves against external attacks. The determination of such admissible sets, depending on specific semantics, is known to be an NP-hard problem. Recent research has demonstrated t...

Inconsistency measurement aims at obtaining a quantitative assessment of the level of inconsistency in knowledge bases. While having such a quantitative assessment is beneficial in various settings, inconsistency measurement of propositional knowledge bases is under most existing measures a significantly challenging computational task. In this work...

Inconsistency measurement aims at obtaining a quantitative assessment of the level of inconsistency in knowledge bases. While having such a quantitative assessment is beneficial in various settings, inconsistency measurement of propositional knowledge bases is under most existing measures a significantly challenging computational task. In this work...

Fifth International Competition on Computational Models of Argumentation (ICCMA'23)

Fifth International Competition on Computational Models of Argumentation (ICCMA'23)

Fifth International Competition on Computational Models of Argumentation (ICCMA'23)

We consider the recently proposed notion of serialisability of semantics for abstract argumentation frameworks. This notion describes a method for the serialised non-deterministic construction of extensions through iterative addition of non-empty minimal admissible sets. Depending on the semantics, the task of enumerating all extensions for an argu...

We consider the recently introduced vacuous reduct semantics in abstract argumentation that allows the composition of arbitrary argumentation semantics through the notion of the reduct. We show that by recursively applying the vacuous reduct scheme we are able to cover a broad range of semantical approaches. Our main result shows that we can recove...

We introduce a novel approach to measure inconsistency in knowledge bases that is based on the Tableau Method and derivations of contradictions from a knowledge base. This approach is purely syntactic and differs from previous approaches by neither taking minimal inconsistent sets nor non-classical semantics into account. We develop three concrete...

We introduce the notion of an undisputed set for abstract argumentation frameworks, which is a conflict-free set of arguments, such that its reduct contains no non-empty admissible set. We show that undisputed sets, and the stronger notion of strongly undisputed sets, provide a meaningful approach to weaken admissibility and deal with the problem o...

We consider the problem of learning argumentation frameworks from a given set of labelings such that every input is a σ-labeling of these argumentation frameworks. Our new algorithm takes labelings and computes attack constraints for each argument that represent the restrictions on argumentation frameworks that are consistent with the input labelin...

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, t...

We address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic (LTL). 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 therefor...

For propositional beliefs, there are well-established connections between belief revision, defeasible condition-als, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic tha...

We introduce the notion of an undisputed set for abstract ar-gumentation frameworks, which is a conflict-free set of arguments , such that its reduct contains no non-empty admissible sets. We show that undisputed sets, and the stronger notion of strongly undisputed sets, provide a meaningful approach to weaken admissibility and deal with the proble...

We propose an algorithm based on satisfiability problem (SAT) solving for determining the contension inconsistency degree in propositional knowledge bases. In addition, we present a revised version of an algorithm based on answer set programming (ASP), which serves the same purpose. In an experimental analysis, we compare the two algorithms to each...

We propose an algorithm based on satisfiability problem (SAT) solving for determining the contension inconsistency degree in propositional knowledge bases. In addition, we present a revised version of an algorithm based on answer set programming (ASP), which serves the same purpose. In an experimental analysis, we compare the two algorithms to each...

We address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic on fixed traces (LTL ff). 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 ope...

We interpret and formalise ordinal conditional functions (OCFs) in abstract argumentation frameworks based on ideas and concepts defined for conditional logics. There, these functions are used to rank interpretations, and we adapt them to rank extensions instead. Using conflict-freeness and admissibility as two essential principles to define the se...

We examine the impact of both training and test data selection in machine learning applications for abstract argumentation, in terms of prediction accuracy and generalizability. For that, we first review previous studies from a data-centric perspective and conduct some experiments to back up our analysis. We further present a novel algorithm to gen...

We investigate the recently proposed notion of serialisability of semantics for abstract argumentation frameworks. This notion describes semantics where the construction of extensions can be serialised through iterative addition of minimal non-empty admissible sets. We investigate general relationships between se-rialisability and other principles...

We introduce probo2, an end-to-end benchmark framework for abstract argumentation solvers. It offers evaluation capabilities and analysis features for a wide range of computational problems and is easily customizable.

We revisit the foundations of ranking semantics for abstract argumenta-tion frameworks by observing that most existing approaches are incompatible with classical extension-based semantics. In particular, most ranking semantics violate the principle of admissibility, meaning that admissible arguments are not necessarily better ranked than inadmissib...

THEIA is a labeling-based system computing the complete extensions of an abstract argumentation framework. Like other backtracking solvers, THEIA does this by repeatedly choosing an argument and labelling it until either a contradiction with respect to the labels is reached or a complete extension is found. THEIA reduces the number of backtracking...

In this paper we present a model for argumentative causal and counterfactual reasoning in a logical setting. Causal knowledge is represented in this system using Pearl's causal model of a set of structural equations and a set of assumptions expressed in propositional logic. Queries concerning observations or actions can be answered by constructing...

We present a dialogical proof theory for credulous acceptance in abstract dialectical frameworks under the preferred semantics. Our approach is motivated by the need to explain why an argument is accepted. The proof theory defines a set of rules for a dialogue between a proponent and opponent exchanging propositional formulas. The proponent takes o...

In this work, we discuss the realisability problem for ranking-based semantics in the area of abstract argumentation. So, for a given ranking and ranking-based semantics, we want to find an AF s.t. the selected ranking-based semantics induces our ranking when applied to the AF. We show that this question can be answered trivially with yes for a num...

We address the task of selecting the fastest algorithm, in terms of run-time, for determining skeptical acceptance under preferred semantics in abstract ar-gumentation frameworks out of a set of multiple algorithms by means of machine learning. To be precise, we examine four "classical" machine learning techniques, as well as three graph neural net...

We address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic on fixed traces (LTL\(_{\text {ff}}\)). 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 th...

We introduce probo2, an end-to-end benchmark framework for abstract argumentation solvers. It offers evaluation capabilities and analysis features for a wide range of computational problems and is easily customizable.

We investigate the recently proposed notion of serialisability of semantics for abstract argumentation frameworks. This notion describes semantics where the construction of extensions can be serialised through iterative addition of minimal non-empty admissible sets. We investigate general relationships between serialisability and other principles f...

We revisit the foundations of ranking semantics for abstract argumentation frameworks by observing that most existing approaches are incompatible with classical extension-based semantics. In particular, most ranking semantics violate the principle of admissibility, meaning that admissible arguments are not necessarily better ranked than inadmissibl...

We interpret and formalise ordinal conditional functions (OCFs) in abstract argumentation frameworks based on ideas and concepts defined for conditional logics. There, these functions are used to rank interpretations, and we adapt them to rank extensions instead. Using conflict-freeness and admissibility as two essential principles to define the se...

We examine the impact of both training and test data selection in machine learning applications for abstract argumentation, in terms of prediction accuracy and generalizability. For that, we first review previous studies from a data-centric perspective and conduct some experiments to back up our analysis. We further present a novel algorithm to gen...

dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical fram...

We revisit the notion of initial sets by Xu and Cayrol [1], 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...

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 oper...

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations , we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logi...

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...

dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialecti-cal fra...

The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We firs...

We present algorithms based on answer set programming (ASP) encodings for solving the problem of determining inconsistency degrees in propositional knowledge bases. For that, we consider the contension inconsistency measure, the forgetting-based inconsistency measure, and the hitting set inconsistency measure. Our experimental evaluation shows that...

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialec-...

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, the question poses itself as to whether some and which monotonic three-valued logic underlies ADFs, in the sense that it allows to capture the main semantic...

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. preferre...

Petri Nets are often used to describe, execute, analyze and improve business processes. A special area of interest is the detection of possible deadlocks. Deadlocks can harm the proper execution of business processes which may lead to errors or even impossible business process execution, and, in turn, economic loss. In most cases, it is only determ...

We investigate the structural patterns of the appearance and disappearance of links in dynamic knowledge networks. Human knowledge is nowadays increasingly created and curated online, in a collaborative and highly dynamic fashion. The knowledge thus created is interlinked in nature, and an important open task is to understand its temporal evolution...

Argumentation is inherently pervaded by uncertainty, which can arise as a result of the context in which argumentation is used, the kinds of agents that are involved in a given situation, the types of arguments that are used, and more. One of the prominent approaches for handling uncertainty in argumentation is probabilistic argumentation, which of...

In abstract argumentation, the admissible semantics can be said to distinguish the preferred semantics in the sense that argumentation frameworks with the same admissible extensions also have the same preferred extensions. In this paper we present an exhaustive study of such distinguishability relationships, including those between sets of semantic...

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures ha...

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that...

We investigate inconsistency and culpability measures for multisets of business rule bases. As companies might encounter thousands of rule bases daily, studying not only individual rule bases separately, but rather also their interrelations, becomes necessary. As current works on inconsistency measurement focus on assessing individual rule bases, w...

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obt...

We address the problem of deciding skeptical acceptance wrt. preferred semantics of an argument in abstract argumentation frameworks, i. e., the problem of deciding whether an argument is contained in all maximally admissible sets, a.k.a. preferred extensions. State-of-the-art algorithms solve this problem with iterative calls to an external SAT- s...

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 necessar...

In this paper we ask whether approximation for abstract argumentation is useful in practice, and in particular whether reasoning with grounded semantics – which has polynomial runtime – is already an approximation approach sufficient for several practical purposes. While it is clear from theoretical results that reasoning with grounded semantics is...

We investigate the notion of independence in abstract argumentation, i.e., the question of whether the evaluation of one set of arguments is independent of the evaluation of another set of arguments, given that we already know the status of a third set of arguments. We provide a semantic definition of this notion and develop a method to discover in...

We investigate the computational problem of determining the set of acceptable arguments in abstract argumentation wrt. credulous and skeptical reasoning under grounded, complete, stable, and preferred semantics. In particular, we investigate the computational complexity of that problem and its verification variant, and develop four SAT-based algori...

We present approximation algorithms for reasoning in struc-tured argumentation approaches such as ASPIC+. While classical approaches consist in constructing all arguments from a knowledge base and determine acceptable arguments from the resulting argument graph, we sample only a small number of arguments and thus only consider a subgraph of the com...

http://www.mthimm.de/pub/2020/Skiba_2020.pdf

We present MINIAF, a general SAT-based abstract argumentation solver that can be used with any SAT solver. We use this general solver to evaluate 12 different SAT solvers wrt. their capability of handling abstract argumentation prob- lems. While our results show that the runtime performance of different SAT solvers are generally comparable, we also...

We consider the problem of quantitatively assessing the conflict between knowledge bases in knowledge merging scenarios. Using the notion of Craig interpolation we define a series of disagreement measures and analyse their compliance with properties proposed in previous work by Potyka. We study basic complexity theoretic questions in that scenario...

Spohnian ranking functions are a qualitative abstraction of probability functions, and they have been applied to knowledge representation and reasoning that involve uncertainty. However, how to represent a ranking function which has a size that is exponential in the number of variables still remains insufficiently explored. In this work we introduc...

We present an algorithm for determining inconsistency degrees wrt. the contension inconsistency measure [7] which utilizes three-valued logic to determine the minimal number of atoms that are assigned truth value B (paradoxical/both true and false). Our algorithm is based on an answer set programming encoding for checking for upper bounds and a bin...

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 argumen...

Machine learning and argumentation can potentially greatly benefit from each other. Combining deep classifiers with knowledge expressed in the form of rules and constraints allows one to leverage different forms of abstractions within argumentation mining. Argumentation for machine learning can yield argumentation-based learning methods where the m...

We address the issue of quantitatively assessing the severity of inconsistencies in non-monotonic frameworks. While measuring inconsistency in classical logics has been investigated for some time now, taking the non-monotonicity into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly K-inconsistent...

We address the issue of analyzing potential inconsistencies in knowledge bases. This refers to knowledge bases that contain rules which will always be activated together, and the knowledge base will become inconsistent, should these rules be activated. We investigate this problem in the context of the industrial use-case of business rule management...

The field of Inconsistency Measurement is concerned with the development of principles and approaches to quantitatively assess the severity of inconsistency in knowledge bases. In this survey, we give a broad overview on this field by outlining its basic motivation and discussing some of these core principles and approaches. We focus on the work th...

We employ graph convolutional networks for the purpose of determining the set of acceptable arguments under preferred semantics in abstract argumentation problems. While the latter problem is complexity-wise one of the hardest problems in reasoning with abstract argumentation problems, approximate methods are needed here in order to obtain a practi...

We apply a selection of 19 inconsistency measures from the literature on artificially generated knowledge bases and study the distribution of their values and their pairwise correlation. This study augments previous analytical evaluations on the expressivity and the pairwise incompatibility of these measures and our findings show that 1.) many meas...

We apply a selection of 19 inconsistency measures from the literature on artificially generated knowledge bases and study the distribution of their values and their pairwise correlation. This study augments previous analytical evaluations on the expressivity and the pairwise incompatibility of these measures and our findings show that (1) many meas...

We employ graph convolutional networks for the purpose of determining the set of acceptable arguments under preferred semantics in abstract argumentation problems. While the latter problem is complexity-wise one of the hardest problems in reasoning with abstract argumentation problems, approximate methods are needed here in order to obtain a practi...