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Matthias Thimm

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68 papers
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68

KR Conference 2025 Conference Paper

A Framework for Inconsistency-tolerant Reasoning with Sets of Models

  • Yehia Hatab
  • Kai Sauerwald
  • Matthias Thimm

We propose a framework for reasoning from inconsistent knowledge bases using minimal hitting sets, i. e. , sets of interpretations such that each formula of the knowledge base is satisfied by at least one those interpretations. By additionally considering preference orders over minimal hitting sets, we can define a wide variety of non-monotonic inference relations. We consider concrete preference orders based on set inclusion, cardinality, the number of conflicting atoms within the hitting set, and using the Hamming distance between pairs of interpretations. We compare the resulting inference relations, characterize their logical properties, and position them relative to classical inference from maximal consistent subsets. Finally, we show that inference based on minimal conflicting atoms coincides with reasoning in Priest’s 3-valued logic.

KR Conference 2025 Conference Paper

A Reduct-based Approach to Skeptical Preferred Reasoning in Abstract Argumentation

  • Lars Bengel
  • Julian Sander
  • Matthias Thimm

We consider abstract argumentation frameworks and, in particular, the problem of skeptical reasoning wrt. preferred semantics, i. e. , deciding whether a given argument is contained in every preferred extension of the argumentation framework. We introduce a novel SAT-based approach, building on recent results from the literature, that searches through complete extensions to efficiently decide this problem. It also employs effective simplification procedures to shorten computation times. As our experimental evaluation shows, our algorithm significantly outperforms state-of-the-art approaches.

JAIR Journal 2025 Journal Article

Comparison of SAT-Based and ASP-Based Algorithms for Inconsistency Measurement

  • Isabelle Kuhlmann
  • Anna Gessler
  • Vivien Laszlo
  • Matthias Thimm

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, forgetting-based, hitting set, max-distance, sum-distance, and hit-distance inconsistency measures. 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.

KR Conference 2025 System Paper

Exploring Desirable Configurations in Global Logistics with Heuristic Search in Answer Set Programming

  • Olcay Altay-Kern
  • Emmanuelle Dietz
  • Isabelle Kuhlmann
  • Matthias Thimm

In the design of global logistics problems, the solution spaces are typically extremely large. To demonstrate how these challenges can be addressed in Answer Set Programming (ASP), this work investigates a representative industrial use case of a global logistics problem in the aerospace problem domain. An exploration of specific areas of the search space is done by using heuristic-driven solving for the formulation of domain heuristics that guide the solver to potentially desirable configurations. A quantitative evaluation on the Key Performance Indicators and a qualitative evaluation on the variability of the models by means of a similarity analysis shows promising results.

IJCAI Conference 2025 Conference Paper

Initial Models and Serialisability in Abstract Dialectical Frameworks

  • Lars Bengel
  • Matthias Thimm

We introduce initial models for abstract dialectical frameworks (ADFs) as a notion of minimal justifiable valuations and based on that, generalise the concept of serialisability of argumentation semantics to ADFs. In particular, we show that the characteristic operator-based semantics for ADFs can be characterised through serialisation sequences, which are, essentially, decompositions of a model into a series of initial models, representing a more fine-grained view into why a model is acceptable wrt. the semantics. We also analyse the computational complexity of tasks related to initial models.

IJCAI Conference 2025 Conference Paper

On Independence and SCC-Recursiveness in Assumption-Based Argumentation

  • Lydia Blümel
  • Anna Rapberger
  • Matthias Thimm
  • Francesca Toni

We introduce a notion of conditional independence in (flat) assumption-based argumentation (ABA), where independence between (sets of) assumptions amounts to the presence of information about one set of assumptions not impacting the acceptability of another. We study general properties, computational complexity, and the relation to independence in abstract argumentation. In light of the high computational complexity of deciding independence, we introduce sound methods for checking independence in polynomial time via two different routes: the first utilizes the strongly connected components (SCCs) of the instantiated abstract argumentation framework; the second exploits the structure of the ABA framework directly. Along the way, we introduce the notion of SCC-recursiveness for ABA.

NMR Workshop 2025 Conference Paper

On Minimal Inconsistent Signatures and their Application to Inconsistency Measurement

  • Matthias Thimm
  • Jandson S. Ribeiro
  • Dennis Peuter
  • Viorica Sofronie-Stokkermans

Minimal inconsistent sets have played an important role in the analysis and general handling of inconsistency in logical knowledge bases. We introduce a semantical counterpart of this notion we call minimal inconsistent signature, which is a minimal set of propositions such that projecting the knowledge base onto it still preserves the inconsistency. We analyse minimal inconsistent signatures and the corresponding dual notion of maximal consistent signatures in depth and show, among others, that the hitting set duality applies for them as well. We apply our new notions to the field of inconsistency measurement and derive a series of new inconsistency measures, which we analyse in terms of postulate satisfaction and general behaviour. Finally, we analyse the computational complexity of various problems within this new context.

KR Conference 2025 Conference Paper

Sequence Explanations for Acceptance in Abstract Argumentation

  • Lars Bengel
  • Matthias Thimm

We consider abstract argumentation and explanations for the acceptance of arguments. Based on the notion of serialisability, we introduce sequence explanations as a procedural form of explanation for the acceptance of some argument. Intuitively, these explanations represent the process of accepting (and rejecting) arguments in order to conclude the acceptance of a certain argument. We define several variants of sequence explanations and examine them in detail. In particular, we also incorporate counterarguments into the explanations to make them dialectical. Finally, we relate our explanations to other approaches from the literature via a principle-based analysis.

NMR Workshop 2025 Conference Paper

Skeptical Preferred Reasoning via Reducts in Abstract Argumentation

  • Lars Bengel
  • Julian Sander
  • Matthias Thimm

We consider abstract argumentation frameworks and, in particular, the problem of skeptical reasoning wrt. preferred semantics, i. e. , deciding whether a given argument is contained in every preferred extension of the argumentation framework. We introduce a novel Sat-based approach, building on recent results from the literature, that searches through complete extensions to efficiently decide this problem. It also employs effective simplification procedures to shorten computation times. As our experimental evaluation shows, our algorithm significantly outperforms current state-of-the-art approaches in most instances.

FLAP Journal 2025 Journal Article

The Semantical Structure of Conditionals, and its Relation to Formal Argumentation

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

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 contem- porary 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 consequent is true in those worlds. Such a subset of possible worlds can represent, for example, the most typical worlds in which the antecedent is true. This idea has proven a fruitful basis, allowing for many systematic characterisation results as well as for making connections to other topics, such as belief revision and modal logic. In formal argumentation, the potential of these semantical ideas has not gone unnoticed in the last years, and

NMR Workshop 2024 Conference Paper

A Hitting Set Approach to Inconsistent-Tolerant Reasoning

  • Yehia Hatab
  • Kai Sauerwald
  • Matthias Thimm

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 based on them. The full landscape of the relationships between the four novel inference relations and the two inferences based on maximal consistent subsets by Rescher and Manor is given. We show that all of the considered inference relations are non-monotonic and satisfy several System P properties. Finally, we show that the respective complexity of inference is at most in the second level of the polynomial hierarchy.

ECAI Conference 2024 Conference Paper

Characterising Serialisation Equivalence for Abstract Argumentation

  • Lars Bengel
  • Julian Sander
  • Matthias Thimm

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 same serialisation sequences. A serialisation sequence is a decomposition of an extension into a series of minimal acceptable sets and essentially offers insight into the order in which arguments need to brought forward to resolve the conflicts and to justify a particular position in the argumentation framework. We analyse serialisation equivalence in detail and show that it is generally more strict than standard equivalence and less strict than strong equivalence. Furthermore, we provide a full analysis of the computational complexity of deciding serialisation equivalence.

KR Conference 2024 Conference Paper

Optimisation and Approximation in Abstract Argumentation: The Case of Admissibility

  • Kenneth Skiba
  • Matthias Thimm

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 optimisation and approximation. Finally, we discuss and analyse soft notions for preferred semantics.

IJCAI Conference 2024 Conference Paper

Optimisation and Approximation in Abstract Argumentation: The Case of Stable Semantics

  • Matthias Thimm

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 investigate the computational complexity of these two problems in terms of the complexity of solving the optimisation problem exactly and in terms of approximation complexity. We also present some polynomial-time approximation algorithms for these optimisation problems and investigate their approximation quality experimentally.

ECAI Conference 2024 Conference Paper

Revisiting Vacuous Reduct Semantics for Abstract Argumentation

  • 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.

KR Conference 2024 Conference Paper

The Realizability of Revision and Contraction Operators in Epistemic Spaces

  • 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, which are a special kind of maxichoice operators. When AGM revision, respectively, AGM contraction, is realizable, linear change operators are a canonical realization.

KR Conference 2023 Conference Paper

Approximating Weakly Preferred Semantics in Abstract Argumentation through Vacuous Reduct Semantics

  • Lydia Blümel
  • Matthias Thimm

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 principle of vacuous reduct semantics we are able to cover a broad range of semantical approaches. Our main result shows that we can recover the weakly preferred semantics as the unique solution of a fixed point equation involving an infinite application of the vacuous reduct semantics based only on the very simple property of conflict-freeness. We also conduct an extensive study of the computational complexity of the recursive application of vacuous reduct semantics, which shows that it completely covers each level of the polynomial hierarchy, depending on the recursion depth.

ECAI Conference 2023 Conference Paper

MaxSAT-Based Inconsistency Measurement

  • Andreas Niskanen
  • Isabelle Kuhlmann
  • Matthias Thimm
  • Matti Järvisalo

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, we harness Boolean satisfiability (SAT) based solving techniques for developing practical inconsistency measurement algorithms. Our algorithms—some of which constitute, to the best of our knowledge, the first practical approaches for specific inconsistency measures—are based on using natural choices of SAT-based techniques for the individual inconsistency measures, ranging from direct maximum satisfiability (MaxSAT) encodings to MaxSAT-based column generation techniques making use of incremental computations. We show through an extensive empirical evaluation that our approaches scale well in practice and significantly outperform recently-proposed answer set programming approaches to inconsistency measurement.

FLAP Journal 2023 Journal Article

Measuring Inconsistency with the Tableau Method.

  • Jandson S. Ribeiro
  • Matthias Thimm

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 measures that take derivations of contradictions into account and investigate their compliance w. r. t. rationality postulates, expressivity, and computational complexity.

AAAI Conference 2023 Conference Paper

On Undisputed Sets in Abstract Argumentation

  • Matthias Thimm

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 of attacks from self-attacking arguments, in a similar manner as the recently introduced notion of weak admissibility. We investigate the properties of our new semantical notions and show certain relationships to classical semantics, in particular that undisputed sets are a generalisation of preferred extensions and strongly undisputed sets are a generalisation of stable extensions. We also investigate the computational complexity of standard reasoning tasks with these new notions and show that they lie on the second and third level of the polynomial hierarchy, respectively.

AIJ Journal 2023 Journal Article

Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

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 keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

KR Conference 2023 Conference Paper

Towards Parallelising Extension Construction for Serialisable Semantics in Abstract Argumentation

  • Lars Bengel
  • Matthias Thimm

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 argumentation framework can be computationally complex. Serialisability provides a natural way of parallelising the construction of extensions for most admissible-based semantics. In this work, we investigate the feasibility of using the serialisable construction scheme for a more efficient enumeration of extensions on the example of the recently introduced unchallenged semantics and provide an experimental evaluation.

AAAI Conference 2022 Conference Paper

Conditional Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Matthias Thimm
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba

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 dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.

IJCAI Conference 2022 Conference Paper

Possibilistic Logic Underlies Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

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 logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

KR Conference 2021 Conference Paper

Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

  • Jandson S. Ribeiro
  • Matthias Thimm

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 have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

KR Conference 2021 Short Paper

Distinguishability in Abstract Argumentation

  • Isabelle Kuhlmann
  • Tjitze Rienstra
  • Lars Bengel
  • Kenneth Skiba
  • Matthias Thimm

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 semantics. We further examine restricted classes of argumentation frameworks, such as self-attack-free and acyclic frameworks. We discuss the relevance of our results in the context of the argumentation framework elicitation problem.

KR Conference 2021 Short Paper

Measuring Inconsistency over Sequences of Business Rule Cases

  • Carl Corea
  • Matthias Thimm
  • Patrick Delfmann

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, we therefore present an extension of those works in the domain of business rules management. We show how arbitrary culpability measures (for single rule bases) can be automatically transformed for multisets, propose new rationality postulates for this setting, and investigate the complexity of central aspects regarding multi-rule base inconsistency measurement.

FLAP Journal 2021 Journal Article

Preface.

  • Dov M. Gabbay
  • Massimiliano Giacomin
  • Guillermo Ricardo Simari
  • Matthias Thimm

IJCAI Conference 2021 Conference Paper

Ranking Extensions in Abstract Argumentation

  • Kenneth Skiba
  • Tjitze Rienstra
  • Matthias Thimm
  • Jesse Heyninck
  • Gabriele Kern-Isberner

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 obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being "more complete'' or "more admissible'' than another. We define a number of general principles to classify extension-ranking semantics and develop concrete approaches. We also study the relation between extension-ranking semantics and argument-ranking based semantics, which rank individual arguments instead of sets of arguments.

KR Conference 2021 Conference Paper

Revision and Conditional Inference for Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

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 keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

IJCAI Conference 2021 Conference Paper

Skeptical Reasoning with Preferred Semantics in Abstract Argumentation without Computing Preferred Extensions

  • Matthias Thimm
  • Federico Cerutti
  • Mauro Vallati

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-solver to determine preferred extensions. We provide a new characterisation of skeptical acceptance wrt. preferred semantics that does not involve the notion of a preferred extension. We then develop a new algorithm that also relies on iterative calls to an external SAT-solver but avoids the costly part of maximising admissible sets. We present the results of an experimental evaluation that shows that this new approach significantly outperforms the state of the art. We also apply similar ideas to develop a new algorithm for computing the ideal extension.

AIJ Journal 2020 Journal Article

Epistemic graphs for representing and reasoning with positive and negative influences of arguments

  • 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.

AIJ Journal 2020 Journal Article

Handling and measuring inconsistency in non-monotonic logics

  • Markus Ulbricht
  • Matthias Thimm
  • Gerhard Brewka

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 subsets of a knowledge base K —a sound generalization of minimal inconsistent subsets to arbitrary, possibly non-monotonic, frameworks which induces a generalization of Reiter's famous hitting set duality between minimal inconsistent and maximal consistent subsets of a knowledge base. We propose measures based on this notion and investigate their behavior in a non-monotonic setting by revisiting existing rationality postulates, analyzing the compliance of the proposed measures with these postulates, and by investigating their computational complexity. Motivated by the observation that a knowledge base of a non-monotonic logic can also be repaired by adding formulas – whereas Reiter's duality is only concerned about removing –, we also investigate situations where we are given potential additional assumptions to repair a knowledge base. For this, we characterize the minimal modifications to a knowledge base in terms of a hitting set duality

KR Conference 2020 Conference Paper

Independence and D-separation in Abstract Argumentation

  • Tjitze Rienstra
  • Matthias Thimm
  • Kristian Kersting
  • Xiaoting Shao

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 independencies based on transforming an argumentation framework into a DAG on which we then apply the well-known d-separation criterion. We also introduce the SCC Markov property for argumentation semantics, which generalises the Markov property from the classical acyclic case and guarantees the soundness of our approach.

AIJ Journal 2020 Journal Article

On quasi-inconsistency and its complexity

  • Carl Corea
  • Matthias Thimm

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, where it is often required that sets of (only) rules are analyzed for potential inconsistencies, e. g. , during business rule modelling. To this aim, we introduce the notion of quasi-inconsistency, which is a formalization of the above-mentioned problem of potential inconsistencies. We put a specific focus on the analysis of computational complexity of some involved problems and show that many of them are intractable.

ECAI Conference 2020 Conference Paper

Towards Inconsistency Measurement in Business Rule Bases

  • 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.

AIJ Journal 2019 Journal Article

On the complexity of inconsistency measurement

  • Matthias Thimm
  • Johannes P. Wallner

We survey a selection of inconsistency measures from the literature and investigate their computational complexity wrt. decision problems related to bounds on the inconsistency value and the functional problem of determining the actual value. Our findings show that those inconsistency measures can be partitioned into four classes related to their complexity. The first three classes contain measures whose complexities are located on the first three levels of the polynomial hierarchy, respectively. The final class is under standard complexity-theoretic assumptions located beyond the polynomial hierarchy. We provide membership results for all the investigated problems and completeness results for most of them. In addition, we undertake a preliminary study on the computational complexity of the measures on fragments of propositional logic.

AIJ Journal 2019 Journal Article

Strong inconsistency

  • Gerhard Brewka
  • Matthias Thimm
  • Markus Ulbricht

Minimal inconsistent subsets of knowledge bases play an important role in propositional logic, most notably for diagnosis, axiom pinpointing, and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play a similar role as minimal inconsistent subsets in propositional logic. In particular, we show that the well-known duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on axiom pinpointing and inconsistency measurement.

KR Conference 2018 Short Paper

A General Approach to Reasoning with Probabilities

  • Federico Cerutti
  • Matthias Thimm

We aim at unifying many of the aforementioned approaches and define a general methodology for reasoning with quantitative uncertainty. This allows for a general study of its properties while abstracting away from any specific instantiation. We focus on probability theory as a means for quantitative uncertain reasoning but a similar methodology can be defined by building on other formalisms such as fuzzy logic or Dempster-Shafer theory. We start by considering an arbitrary base logic and define its probabilistic augmentation by extending the syntax to allow for annotated probabilities on each formula. Therefore, a knowledge base of probabilistic augmentation consists of a set of formulas, each annotated with a probability. We define a general probabilistic semantics on top of the built-in semantics of the base logic by (1) considering each subset of the knowledge base, (2) performing ordinary inference within the subset, and (3) accumulating the inferences by taking the probabilities into account. This gives us a general methodology for defining probabilistic versions of existing knowledge representation formalisms, and is inspired by many concrete realisations such as the distribution semantics for logic programming (Sato 1995). We propose a general scheme for adding probabilistic reasoning capabilities to any knowledge representation formalism.

AAAI Conference 2018 Conference Paper

Measuring Strong Inconsistency

  • Markus Ulbricht
  • Matthias Thimm
  • Gerhard Brewka

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 K-inconsistent subsets of a knowledge base K—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.

KR Conference 2018 Conference Paper

Probabilistic Abstract Argumentation based on SCC Decomposability

  • Tjitze Rienstra
  • Matthias Thimm
  • Beishui Liao
  • Leendert van der Torre

In this paper we introduce a new set of general principles for probabilistic abstract argumentation. The main principle is a probabilistic analogue of SCC decomposability, which ensures that the probabilistic evaluation of an argumentation framework complies with the probabilistic (in)dependencies implied by the graph topology. We introduce various examples of probabilistic semantics and determine which principles they satisfy. Our work also provides new insights into the relationship between abstract argumentation and the theory of Bayesian networks.

FLAP Journal 2017 Journal Article

Foundations of Implementations for Formal Argumentation.

  • Federico Cerutti
  • Sarah Alice Gaggl
  • Matthias Thimm
  • Johannes P. Wallner

We survey the current state of the art of general techniques, as well as specific software systems for solving tasks in abstract argumentation frameworks, structured argumentation frameworks, and approaches for visualizing and analysing argumentation. Furthermore, we discuss challenges and promising techniques such as parallel processing and approximation approaches. Finally, we address the issue of evaluating software systems empirically with links to the International Competition on Computational Models of Argumentation.

IJCAI Conference 2017 Conference Paper

On the Expressivity of Inconsistency Measures (Extended Abstract)

  • Matthias Thimm

We survey recent approaches to inconsistency measurement in propositional logic and provide a comparative analysis in terms of their expressivity. For that, we introduce four different expressivity characteristics that quantitatively assess the number of different knowledge bases that a measure can distinguish. Our approach aims at complementing ongoing discussions on rationality postulates for inconsistency measures by considering expressivity as a desirable property. We evaluate a large selection of measures on the proposed characteristics and conclude that a distance-based measure from [Grant and Hunter, 2013] has maximal expressivity along all considered characteristics.

JAIR Journal 2017 Journal Article

Probabilistic Reasoning with Abstract Argumentation Frameworks

  • Anthony Hunter
  • Matthias Thimm

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.

IJCAI Conference 2017 Conference Paper

Strong Inconsistency in Nonmonotonic Reasoning

  • Gerhard Brewka
  • Matthias Thimm
  • Markus Ulbricht

Minimal inconsistent subsets of knowledge bases play an important role in classical logics, most notably for repair and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play the same role as minimal inconsistent subsets in classical reasoning. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on repair and inconsistency measurement.

AIJ Journal 2017 Journal Article

The first international competition on computational models of argumentation: Results and analysis

  • Matthias Thimm
  • Serena Villata

We report on the First International Competition on Computational Models of Argumentation (ICCMA'15) which took place in the first half of 2015 and focused on reasoning tasks in abstract argumentation frameworks. Performance of submitted solvers was evaluated on four computational problems wrt. four different semantics relating to the verification of the acceptance status of arguments, and computing jointly acceptable sets of arguments. In this paper, we describe the technical setup of the competition, and give an overview on the submitted solvers. Moreover, we report on the results and discuss our findings.

IJCAI Conference 2016 Conference Paper

Group Decision Making via Probabilistic Belief Merging

  • Nico Potyka
  • Erman Acar
  • Matthias Thimm
  • Heiner Stuckenschmidt

We propose a probabilistic-logical framework for group decision-making. Its main characteristic is that we derive group preferences from agents' beliefs and utilities rather than from their individual preferences as done in social choice approaches. This can be more appropriate when the individual preferences hide too much of the individuals' opinions that determined their preferences. We introduce three preference relations and investigate the relationships between the group preferences and individual and subgroup preferences.

JELIA Conference 2016 Conference Paper

Measuring Inconsistency in Answer Set Programs

  • Markus Ulbricht 0001
  • Matthias Thimm
  • Gerhard Brewka

Abstract We address the issue of quantitatively assessing the severity of inconsistencies in logic programs under the answer set semantics. While measuring inconsistency in classical logics has been investigated for some time now, taking the non-monotonicity of answer set semantics into account brings new challenges that have to be addressed by reasonable accounts of inconsistency measures. We investigate the behavior of inconsistency in logic programs by revisiting existing rationality postulates for inconsistency measurement and developing novel ones taking non-monotonicity into account. Further, we develop new measures for this setting and investigate their properties.

KR Conference 2016 Conference Paper

On Partial Information and Contradictions in Probabilistic Abstract Argumentation

  • Anthony Hunter
  • Matthias Thimm

We provide new insights into the area of combining abstract argumentation frameworks with probabilistic reasoning. In particular, we consider the scenario when assessments on the probabilities of a subset of the arguments is 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 generalize 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 inconsistent-tolerant reasoning.

AIJ Journal 2016 Journal Article

On the expressivity of inconsistency measures

  • Matthias Thimm

We survey recent approaches to inconsistency measurement in propositional logic and provide a comparative analysis in terms of their expressivity. For that, we introduce four different expressivity characteristics that quantitatively assess the number of different knowledge bases that a measure can distinguish. Our approach aims at complementing ongoing discussions on rationality postulates for inconsistency measures by considering expressivity as a desirable property. We evaluate 16 different measures on the proposed characteristics and conclude that the distance-based measure I dalal Σ from Grant and Hunter (2013) [8] and the proof-based measure I P m from Jabbour and Raddaoui (2013) [16] have maximal expressivity along all considered characteristics. In our study, we discovered several interesting relationships of inconsistency measurement to e. g. set theory and Boolean functions and we also report these findings.

KR Conference 2016 Conference Paper

Some Complexity Results on Inconsistency Measurement

  • Matthias Thimm
  • Johannes P. Wallner

We survey a selection of inconsistency measures from the literature and investigate their computational complexity wrt. decision problems related to bounds on the inconsistency value and the functional problem of determining the actual value. Our findings show that those inconsistency measures can be partitioned into three classes related to their complexity. The first class contains measures whose complexity are located on the first level of the polynomial hierarchy, the second class contains measures on the second level of the polynomial hierarchy, and the third class is located beyond the second level of the polynomial hierarchy. We provide membership results for all the investigated problems and completeness results for most of them. 1 In this paper, we address the computational complexity of inconsistency measurement by investigating a selection of 13 inconsistency measures for propositional logic from the literature mentioned above. Inconsistency measurement is, by definition, a computationally intractable problem as it goes beyond merely detecting inconsistency (which is itself an coNP-complete problem for propositional logic). However, no systematic investigation of the complexity of inconsistency measures—and a comparison of measures wrt. it—has been conducted so far. The only complexity analyses on inconsistency measures we are aware of were presented in (Ma et al. 2010) and (Xiao and Ma 2012) and each focused on a particular inconsistency measure. In (Ma et al. 2010) the complexity of a variant of the contension inconsistency measure Ic (Grant and Hunter 2011) and in (Xiao and Ma 2012) the complexity of the measure Imv from (Xiao and Ma 2012) itself are investigated (we will recall the formal definitions of these measures in Sec. 3 and the corresponding results in Sec. 4, respectively). Recently, the algorithmic challenges in computing inconsistency measures have gained some attention (Ma et al. 2010; McAreavey, Liu, and Miller 2014; Thimm 2016b) and therefore calls for a theoretical investigation on the complexity of the involved computational problems. In this paper, we take a first step in this direction by providing a detailed analysis on the computational complexity of 13 measures wrt. three decision problems, namely deciding whether a given value is an upper, resp. lower bound, or is the exact value, as well as the functional problem of determining the inconsistency value. We mainly focus on the decision problems of deciding whether a given value is an upper, or resp. a lower bound, since, as we will see, the complexity classification of these decision problems gives crucial insights into the computational complexity of the inconsistency measure at hand.

IJCAI Conference 2015 Conference Paper

Probabilistic Reasoning with Inconsistent Beliefs Using Inconsistency Measures

  • Nico Potyka
  • Matthias Thimm

The classical probabilistic entailment problem is to determine upper and lower bounds on the probability of formulas, given a consistent set of probabilistic assertions. We generalize this problem by omitting the consistency assumption and, thus, provide a general framework for probabilistic reasoning under inconsistency. To do so, we utilize inconsistency measures to determine probability functions that are closest to satisfying the knowledge base. We illustrate our approach on several examples and show that it has both nice formal and computational properties.

ECAI Conference 2014 Conference Paper

Coherence and Compatibility of Markov Logic Networks

  • Matthias Thimm

Markov logic is a robust approach for probabilistic relational knowledge representation that uses a log-linear model of weighted first-order formulas for probabilistic reasoning. This log-linear model always exists but may not represent the knowledge engineer's intentions adequately. In this paper, we develop a general framework for measuring this coherence of Markov logic networks by comparing the resulting probabilities in the model with the weights given to the formulas. Our measure takes the interdependence of different formulas into account and analyzes the degree of impact they have on the probabilities of other formulas. This approach can be used by the knowledge engineer in constructing a well-formed Markov logic network if data for learning is not available. We also apply our approach to the problem of assessing the compatibility of multiple Markov Logic networks, i. e. , to measure to what extent the merging of these networks results in a change of probabilities.

ECAI Conference 2014 Conference Paper

Consolidation of Probabilistic Knowledge Bases by Inconsistency Minimization

  • Nico Potyka
  • Matthias Thimm

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.

ECAI Conference 2014 Conference Paper

Probabilistic Argumentation with Incomplete Information

  • Anthony Hunter
  • Matthias Thimm

We consider augmenting abstract argumentation frame-works 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.

KR Conference 2014 Conference Paper

Tweety: A Comprehensive Collection of Java Libraries for Logical Aspects of Artificial Intelligence and Knowledge Representation

  • Matthias Thimm

can build formulas which are collected in knowledge bases. Using knowledge bases one can derive new information using either the underlying semantics of the language or a specific reasoner. For example, propositional logic is the most basic form for knowledge representation. Given some set of propositions (or atoms) one can build complex formulas using disjunction, conjunction, or negation. A set of propositional formulas, i. e., a knowledge base, can be used to derive new propositional formulas as conclusions. For instance, this can be done using the standard model-theoretic semantics of propositional logic or more sophisticated reasoning techniques such as paraconsistent reasoning. Most logical approaches to knowledge representation such as firstorder logic, description logics, defeasible logics, default logics, probabilistic logics, fuzzy logics, etc. follow this pattern. Moreover, many other formalisms which are not so obviously rooted in logic such as abstract argumentation or Bayes nets can also be cast into this framework. For example, for abstract argumentation frameworks [Dung, 1995], a knowledge base is given by a conjunction of attack statements between arguments and different kinds of semantics such as grounded or stable semantics determine how sets of arguments can be derived from a knowledge base. The Tweety libraries support the implementation of such approaches by providing a couple of abstract classes and interfaces for components such as Formula, BeliefBase, and Reasoner. Furthermore, many strictly logic-based approaches to knowledge representation can also utilize further classes such as Predicate, Atom, and Variable, to name just a few. Currently, Tweety already contains implementations of over 15 different approaches to knowledge representation such as propositional logic, first-order logic, several approaches to probabilistic logics, and several approaches to computational models of argumentation. In this paper, besides giving an overview on the technical details of Tweety and its libraries, we also report on two case studies that use Tweety as a framework for experimentation and empirical evaluation. The first study is on inconsistency measurement for probabilistic logics [Thimm, 2011; 2013b]. In general, probabilistic logics are concerned with using quantitative uncertainty for non-monotonic reasoning. Naturally, these approaches are computationally hard and not easy to understand, as the underlying reasoning mechanisms are quite complicated. Consequently, implementa- 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.

AIJ Journal 2013 Journal Article

Inconsistency measures for probabilistic logics

  • Matthias Thimm

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.

IJCAI Conference 2013 Conference Paper

Opponent Models with Uncertainty for Strategic Argumentation

  • Tjitze Rienstra
  • Matthias Thimm
  • Nir Oren

This paper deals with the issue of strategic argumentation in the setting of Dung-style abstract argumentation theory. Such reasoning takes place through the use of opponent models—recursive representations of an agent’s knowledge and beliefs regarding the opponent’s knowledge. Using such models, we present three approaches to reasoning. The first directly utilises the opponent model to identify the best move to advance in a dialogue. The second extends our basic approach through the use of quantitative uncertainty over the opponent’s model. The final extension introduces virtual arguments into the opponent’s reasoning process. Such arguments are unknown to the agent, but presumed to exist and interact with known arguments. They are therefore used to add a primitive notion of risk to the agent’s reasoning. We have implemented our models and we have performed an empirical analysis that shows that this added expressivity improves the performance of an agent in a dialogue.

ECAI Conference 2012 Conference Paper

A Probabilistic Semantics for abstract Argumentation

  • Matthias Thimm

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.

ECAI Conference 2012 Conference Paper

A Ranking Semantics for First-Order Conditionals

  • Gabriele Kern-Isberner
  • Matthias Thimm

Usually, default rules in the form of conditional statements are built on propositional logic, representing classes of individuals by propositional variables, as in "Birds fly, but penguins don't". Only few approaches have addressed the problem of giving formal semantics to first-order conditionals that allow (nonmonotonic) inferences both for classes and for individuals. In this paper, we present a semantics for first-order conditionals that is based on ordinal conditional (or ranking) functions which are well-known in the area of propositional default reasoning and makes use of representative individuals to establish conditional relationships. We generalize the c-representation approach of [8] for inductive reasoning with first-order conditionals, and evaluate our approach via benchmark examples and a catalogue of general properties.

AAMAS Conference 2010 Conference Paper

Classification and Strategical Issues of Argumentation Games on Structured Argumentation Frameworks

  • Matthias Thimm
  • Alejandro J. Garcia

This paper aims at giving a classification of argumentationgames agents play within a multi-agent setting. We investigate different scenarios of such argumentation games thatdiffer in the protocol used for argumentation, i. e. direct, synchronous, and dialectical argumentation protocols, theawareness that agents have on other agents beliefs, and different settings for the preferences of agents. To this endwe employ structured argumentation frameworks, which arean extension to Dung's abstract argumentation frameworksthat give a simple inner structure to arguments. We alsoprovide some game theoretical results that characterize aspecific argumentation game as strategy-proof and developsome argumentation selection strategies that turn out tobe the dominant strategies for other specific argumentationgames.

KR Conference 2010 Conference Paper

Novel Semantical Approaches to Relational Probabilistic Conditionals

  • Gabriele Kern-Isberner
  • Matthias Thimm

It seems to be a common view that in order to interpret probabilistic first-order sentences, either a statistical approach that counts (tuples of) individuals has to be used, or the knowledge base has to be grounded to make a possible worlds semantics applicable, for a subjective interpretation of probabilities. In this paper, we propose novel semantical perspectives on first-order (or relational) probabilistic conditionals that are motivated by considering them as subjective, but populationbased statements. We propose two different semantics for relational probabilistic conditionals, and a set of postulates for suitable inference operators in this framework. Finally, we present two inference operators by applying the maximum entropy principle to the respective model theories. Both operators are shown to yield reasonable inferences according to the postulates.

UAI Conference 2009 Conference Paper

Measuring Inconsistency in Probabilistic Knowledge Bases

  • 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.

AAMAS Conference 2008 Conference Paper

Belief Operations for Motivated BDI Agents

  • Patrick Kr
  • uuml; mpelmann
  • Matthias Thimm
  • Gabriele Kern-Isberner
  • Manuela Ritterskamp

The beliefs of an agent reflecting her subjective view of the world constitute one of the main components of a BDI agent. In order to incorporate new information coming from other agents, or to adjust to changes in the environment, the agent has to carry out belief change operations while taking metalogical information on time and reliabilities into account. In this paper, we describe a framework for belief operations within a BDI agent, sketching the interactions of beliefs with desires and intentions, respectively. Furthermore, we illustrate how motivations and know-how come into play in our agent model of this framework. We focus on the presentation of a complex setting for belief change that makes use of techniques both from merging and update, and provides a BDI agent with advanced reasoning capabilities. Extended logic programs under the answer set semantics will serve as the basic knowledge representation formalism.

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