Ringo Baumann

• Professor
• Heisenbergprofessor at Leipzig University

The topic of forgetting, which loosely speaking means losing, removing, or even hiding some variables, propositions, or formulas, has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. In this article, we convey this topic to the highly active field of abstract argumentation. We provide an in-...

Argument mining usually operates on short, decontextualized argumentative units such as main and subordinate clauses, or full sentences as proxies for arguments. Argumentation in digital media environments , however, is embedded in larger contexts. Especially on social media platforms, argumentation unfolds in dialog threads or tree structures wher...

The paper deals with the topic of realizability in abstract argumentation. More precisely, we consider the most basic kind of labellings, so-called conflict-free labellings. The understanding of these labellings is essential as any mature labelling-based semantics selects its output among these labellings. We show how to decide whether a given set...

dialectical frameworks (ADFs) are one of the most powerful generalizations of classical Dung-style argumentation frameworks (AFs). The additional expressive power comes with an increase in computational complexity, namely one level up in the polynomial hierarchy in comparison to their AF counterparts. However, there is one important subclass, so-ca...

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claima...

The distinction between explicit and implicit information is essential in knowledge representation. In case of argumentation frameworks (AFs) the latter comes to light if dynamics are considered. The study of dynamic involvements is one of the most active fields in argumentation theory in recent years. In this paper, we further contribute to this t...

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration are claim...

In his seminal 1995 paper, Dung laid the foundations of abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd att...

The topic of forgetting has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. Quite recently it has been introduced to abstract argumentation. However, many already known as well as essential aspects about forgetting like strong persistence or strong invariance have been left unconsidered. We...

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claim-...

Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism, since it allows to locally replace parts of a given theory without changing its meaning. In contrast to classical logic, where strong equivalence coincides with standard equiv...

The topic of forgetting has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. Quite recently it has been introduced to abstract ar-gumentation. However, many already known as well as essential aspects about forgetting like strong persistence or strong invariance have been left unconsidered. M...

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration are claim...

We develop a notion of explanations for acceptance of arguments in an abstract argumentation framework. To this end we show that extensions returned by Dung's standard semantics can be decomposed into i) non-deterministic choices made on even cycles of the given argumentation graph and then ii) deterministic iteration of the so-called characteristi...

Within argumentation dynamics, a major strand of research is concerned with how changing an argumentation framework affects the acceptability of arguments, and how to modify an argumentation framework in order to guarantee that some arguments have a given acceptance status. In this chapter, we overview the main approaches for enforcement in formal...

argumentation as defined by Dung in his seminal 1995 paper is by now a major research area in knowledge representation and reasoning. Dynamics of abstract argumentation frameworks (AFs) as well as syntactical consequences of semantical facts of them are the central issues of this paper. The first main part is engaged with the systematical study of...

Semantics based on weak admissibility were recently introduced to overcome a problem with self-defeating arguments that has not been solved for more than 25 years. The recursive definition of weak admissibility mainly relies on the notion of a reduct regarding a set E which only contains arguments which are neither in E, nor attacked by E. At first...

We introduce a Python script for an easy and intuitive calculation of semantics of Abstract Dialectical Frameworks (ADFs) with arbitrary acceptance conditions. In addition, the script enables the evaluation of so-called single-node formulae with the help of Kleene's three-valued logic. The experimental results show that we achieve an enormous compu...

We introduce a Python script for an easy and intuitive calculation of semantics of Abstract Dialectical Frameworks (ADFs) with arbitrary acceptance conditions. In addition, the script enables the evaluation of so-called single-node formulae with the help of Kleene's three-valued logic. The experimental results show that we achieve an enormous compu...

dialectical frameworks (ADFs) are one of the most powerful generalization of classical Dung-style AFs. In this paper we show how to use ADFs if we want to deal with acceptance conditions changing over time. We therefore introduce so-called timed abstract di-alectical frameworks (tADFs) which are essentially ADFs equipped with time states. Beside a...

Semantics based on weak admissibility were recently introduced to overcome a problem with self-defeating arguments that has not been solved for more than 25 years. The recur-sive definition of weak admissibility mainly relies on the notion of a reduct regarding a set E which only contains arguments which are neither in E, nor attacked by E. At firs...

Two different perspectives on argumentation have been pursued in computer science research, namely approaches of argument mining in natural language processing on the one hand, and formal argument evaluation on the other hand. So far these research areas are largely independent and unrelated. This article introduces the agenda of our recently start...

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axioma...

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack lo...

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its...

Conflicting information in an agent's knowledge base may lead to a semantical defect, that is, a situation where it is impossible to draw any plausible conclusion. Finding out the reasons for the observed inconsistency (so-called diagnoses) and/or restoring consistency in a certain minimal way (so-called repairs) are frequently occurring issues in...

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its...

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axioma...

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack lo...

The General Formal Ontology (GFO) is a top-level ontology that includes theories of time and space, two domains of entities of fundamental character. In this connection the axiomatic theories of GFO are based on the relation of coincidence, which can apply to the boundaries of time and space entities. Two co-incident, but distinct boundaries accoun...

This paper continues the rather recent line of research on the dynamics of non-monotonic formalisms. In particular, we consider semantic changes in Dung’s abstract argumentation formalism. One of the most studied problems in this context is the so-called enforcing problem which is concerned with manipulating argumentation frameworks (AFs) such that...

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. We also provide exac...

This chapter is devoted to argumentation semantics which play the flagship role in Dung's abstract argumentation theory. Almost all of them are motivated by an easily understandable intuition of what should be acceptable in the light of conflicts. However, although these intuitions equip us with short and comprehensible formal definitions it turned...

The aim of the paper is to combine two of the most important areas of knowledge representation, namely belief revision and argumen-tation. We present a first study of AGM-style contraction for abstract ar-gumentation frameworks (AFs). Contraction deals with removing former beliefs from a given knowledge base. Our presented approach is based on a re...

Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism since it allows one to locally replace, and thus give rise for simplification , parts of a given theory without changing the semantics of the latter. In contrast to classical l...

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argu-mentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. We also provide exa...

Conflicting information in an agent's knowledge base may lead to a semantical defect, that is, a situation where it is impossible to draw any plausible conclusion. Finding out the reasons for the observed inconsistency (so-called diagnosis) and/or restoring consistency in a certain minimal way (so-called repairs) are frequently occurring issues in...

This paper continues the rather recent line of research on the dynamics of non-monotonic formalisms. In particular, we consider semantic changes in Dung's abstract argumentation formalism. One of the most studied problems in this context is the so-called enforcing problem which is concerned with manipulating argumentation frameworks (AFs) such that...

Conflicting information in an agent's knowledge base may lead to a semantical defect, that is, a situation where it is impossible to draw any plausible conclusion. Finding out the reasons for the observed inconsistency (so-called diagnosis) and/or restoring consistency in a certain minimal way (so-called repairs) are frequently occurring issues in...

A Boolean function is bipolar iff it is monotone or anti-monotone in each of its arguments.We investigate the number b(n) of n-ary bipolar Boolean functions.We present an (almost) closed-form expression for b(n) that uses the number a(n) of antichain covers of an n-element set. This is closely related to Dedekind's problem, which can be rephrased a...

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this...

Research in abstract argumentation typically per-tains to finite argumentation frameworks (AFs). Ac-tual or potential infinite AFs frequently occur if theyare used for the purpose of nonmonotonic entail-ment, so-called instantiation-based argumentation,or if they are involved as modeling tool for dia-logues, n-person-games or action sequences. Apar...

argumentation frameworks (AFs) are one of the most studied formalisms in AI and are formally simple tools to model arguments and their conflicts. The evaluation of an AF yields extensions (with respect to a semantics) representing alternative acceptable sets of arguments. For many of the available semantics two effects can be observed: there exist...

Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by so-called argumentation frameworks (AFs) and the reasoning is done via semantics extracting acceptable sets. All reasonable semantics are based on the notion of conflict...

A central question in knowledge representation is the following: given some knowledge representation formalism, is it possible, and if so how, to simplify parts of a knowledge base without affecting its meaning, even in the light of additional information? The term strong equivalence was coined in the literature, i.e. strongly equivalent knowledge...

Space and time are basic categories of any top-level ontology. They account for fundamental assumptions of the modes of existence of those individuals that are said to be in space and time. The present paper is devoted to GFO-Space, the ontology of space in the General Formal Ontology (GFO). This ontology is introduced by a set of axioms formalized...

argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by argumentation frameworks (AFs) and the reasoning is done via semantics extracting acceptable sets. All reasonable semantics are based on the notion of conflict-freeness which means that...

Notions of equivalence that are stronger than standard equivalence in the sense that they also take potential modifications of the available information into account have received considerable interest in non-monotonic reasoning. In this article, we focus on equivalence notions in argumentation. More specifically, we establish a number of new resul...

Abstract properties satisfied for finite structures do not necessarily carry over to infinite structures. Two of the most basic properties are existence and uniqueness of something. In this work we study these properties for acceptable sets of arguments, so-called extensions, in the field of abstract argumentation. We review already known results,...

We give a list of currently unsolved problems in abstract argumentation. For each of the problems, we motivate why it is interesting and what makes it (apparently) hard to solve.

In this paper we combine two of the most important areas of knowledge representation, namely belief revision and (abstract) argumentation. More pre- cisely, we show how AGM-style expansion and re- vision operators can be defined for Dung’s abstract argumentation frameworks (AFs). Our approach is based on a reformulation of the original AGM postulat...

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a...

We present an analytical and empirical study of the maximal and average numbers of stable extensions in abstract argumentation frameworks. As one of the analytical main results, we prove a tight upper bound on the maximal number of stable extensions that depends only on the number of arguments in the framework. More interestingly, our empirical res...

A special case of loops in argumentation are self-attacking arguments. While their role with respect to the ontological nature of argumentation is controversially discussed, their presence (or absence) in the abstract setting of Dung-style argumentation frameworks seems to be less crucial for semantics or fundamental properties. There are, however,...

Time is a pervasive notion of high impact in information systems and computer science altogether. Respective understandings of the domain of time are fundamental for numerous areas, frequently in combination with closely related entities such as events, changes and processes. The conception and representation of time entities and reasoning about te...

Notions of equivalence which guarantee intersubstitutability w.r.t. further modifications have received considerable interest in nonmonotonic reasoning. This paper is within the context of abstract argumentation and we focus on the most general form of a dynamic scenarios, so-called updates as well as certain sub-classes, namely local, normal and a...

Notions of equivalence which are stronger than standard equivalence in the sense that they also take potential modifications of the available information into account have received considerable interest in nonmonotonic reasoning. In this paper we focus on equivalence notions in argumentation. More specifically, we establish a number of new results...

In this paper we present various new results related to the dynamics of abstract argumentation. Baumann [1] studied the effort needed to enforce a set of arguments E, measured in terms of the minimal number of modifications needed to turn an argumentation framework (AF) \(\mathcal{A}\) into a framework \(\mathcal{A}^*\) such that \(\mathcal{A}^*\)...

Given a semantics σ, two argumentation frameworks (AFs) FF and GG are said to be standard equivalent if they possess the same extensions and strongly equivalent if, for any AF HH, FF conjoined with HH and GG conjoined with HH are standard equivalent. Argumentation is a dynamic process and, in general, new arguments occur in response to a former arg...

Time, events, changes and processes play a major role in conceptual modeling, and in information systems and computer science altogether. Accordingly, the representation of time structures and reasoning about temporal data and knowledge are important theoretical and practical research areas. We assume that a formal representation of temporal knowle...

In an important and much cited paper Vladimir Lifschitz and Hudson Turner have shown how, under certain conditions, logic programs under answer set semantics can be split into two disjoint parts, a “bottom” part and a “top” part. The bottom part can be evaluated independently of the top part. Results of the evaluation, i.e., answer sets of the bott...

Reasoning about actions is a subfield of artificial intelligence that is concerned with representing and reasoning about dynamic domains. We propose to employ abstract argumentation for this purpose. Specifically, we present a translation of action domains from a specification language into Dung-style argumentation frameworks (AFs). As the key adva...

Argumentation is a dynamic process. The enforcing problem in argumentation, i.e. the question whether it is possible to modify a given argumentation framework (AF) in such a way that a desired set of arguments becomes an extension or a subset of an extension, was first studied in and positively answered under certain conditions. In this paper, we t...

Space and time are basic categories of any top-level ontology. They are fundamental assumptions for the mode of existence of those individuals which are said to be in space and time. In the present paper the ontology of space in the General Formal Ontology (GFO) is expounded. This ontology is represented as a theory BT (Brentano Theory), which is s...

In a recent paper Baumann [1] has shown that splitting results, similar to those known for logic programs under answer set semantics and default logic, can also be obtained for Dung argumentation frameworks (AFs). Under certain conditions a given AF A can be split into subparts A 1 and A 2 such that extensions of A can be computed by (1) computing...

Splitting results in non-mononotonic formalisms have a long tradition. On the one hand, these results can be used to improve existing computational procedures, and on the other hand they yield deeper theoretical insights into how a non-monotonic approach works. In the 90‘s Lifschitz and Turner [1,2] proved splitting results for logic programs and d...

We present a framework for reasoning about actions that not only solves the frame and ramification problems, but also the state default problem-the problem to determine what normally holds at a given time point. Yet, the framework is general enough not to be tied to a specific time structure. This is achieved as follows: We use effect axioms that d...

This paper addresses the problem of revising a Dung-style argumentation framework by adding finitely many new arguments which may interact with old ones. We study the behavior of the extensions of the augmented argumentation frameworks, taking also into account possible changes of the underlying semantics (which may be interpreted as corresponding...

This paper addresses the problem of revising a Dung-style argumentation framework by adding finitely many new arguments which may interact with old ones. We study the behavior of the extensions of the augmented argumentation frameworks, taking also into account possible changes of the underlying semantics (which may be interpreted as corresponding...