Gabriele Kern-Isberner

Technische Universität Dortmund | TUD · Faculty of Computer Science

Splitting belief bases is fundamental for efficient reasoning and for better understanding interrelationships among the knowledge entities. In this paper, we survey the most important splitting techniques for conditional belief bases in the context of c-representations which constitute a specific class of ranking models with outstanding behavior no...

The class of inductive inference operators that extend rational closure, as introduced by Lehmann or via Pearl’s system Z, exhibits desirable inference characteristics. The property that formalizes this, known as (RC Extension), has recently been investigated for basic defeasible entailment relations. In this paper, we explore (RC Extension) for mo...

Representing knowledge in a comprehensible and maintainable way and transparently providing inferences thereof are important issues, especially in the context of applications related to artificial intelligence in medicine. This becomes even more obvious if the knowledge is dynamically growing and changing and when machine learning techniques are be...

Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as con...

New information in the context of real life settings usually is accompanied by some kind of supplementary information that indicates context, reliability, or expertise of the information's source. Bounded Revision (BR) displays an iterated belief revision mechanism that takes as input a new information accompanied by a reference sentence acting as...

Answer set programming (ASP) and conditional reasoning both are powerful and widely used methodologies from the field of knowledge representation and reasoning (KR) which are capable of formalizing default statements that usually hold but also leave room for exceptions. While ASP convinces with an intuitive rule-based syntax and fast solvers, condi...

In this paper, we apply answer set programming (ASP) to the task of planning warehouse layouts within the logistical domain. Warehouse layout planners have to take into account a vast number of aspects to come up with feasible layouts, especially the placement of logistical elements under specific conditions like the accessibility of warehouse elem...

The recently introduced notion of an inductive inference operator captures the process of completing a given conditional belief base to an inference relation. System W is such an inductive inference operator exhibiting some notable properties like extending rational closure and satisfying syntax splitting for inference from conditional belief bases...

A minimum requirement of feasible order picking layouts is the accessibility of every storage location. Obeying only this requirement typically leads to a vast amount of different layouts that are theoretically possible. Being able to generate all of these layouts automatically opens the door for new layouts and is valuable training data for reinfo...

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...

In probabilistic belief revision, the kinematics principle is a well-known and powerful principle which ensures that changing the probabilities of facts does not change unnecessarily conditional probabilities. A related principle, the principle of conditional preservation, has also been one of the main guidelines for the axioms of iterated belief r...

In this paper, we bring together marginalization and forgetting of signature elements in the framework of epistemic states. Marginalization of epistemic states is a specific approach to actively reduce signatures, also aiming at forgetting atoms which are very well known from probability theory. On the other hand, rooted in Boole’s variable elimina...

Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $\m...

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...

Using answer set programming in real-world applications requires that the answer set program is correct and adequately represents knowledge. In this paper, we present strategies to resolve unintended contradictory statements resulting from modelling gaps and other flaws by modifying the program without manipulating the actual conflicting rules (inc...

Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $\m...

Conditional independence is a crucial concept for efficient probabilistic reasoning. For symbolic and qualitative reasoning, however, it has played only a minor role. Recently, Lynn, Delgrande, and Peppas have considered conditional independence in terms of syntactic multivalued dependencies. In this paper, we define conditional independence as a s...

Revision by Comparison (RbC) is a non-prioritized belief revision mechanism on epistemic states that specifies constraints on the plausibility of an input sentence via a designated reference sentence, allowing for kind of relative belief revision. In this paper, we make the strategy underlying RbC more explicit and transfer the mechanism together w...

Lexicographic inference is a well-known and popular approach to reasoning with non-monotonic conditionals. It is a logic of very high-quality, as it extends rational closure and avoids the so-called drowning problem. It seems, however, this high quality comes at a cost, as reasoning on the basis of lexicographic inference is of high computational c...

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...

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...

Many modern artificial intelligence (AI) systems like human-interacting smart devices or expert systems adapt to specific users' information processes but the underlying AI methods commonly lack a theory of mind. Thus, there is a need to better understand human thinking and to integrate the resulting cognitive models into AI methods. By taking the...

In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for contraction which consider the dynamics of conditional beliefs. For all these principles, we provide semantic cha...

Combining a line production with a matrix production into a hybrid production is a vivid field of research to cope with the challenges of mass personalization. Nevertheless, to implement a hybrid system, several challenges have to be overcome. For a line production, a predefined sequence of products is necessary in order to handle variants at all....

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...

Generating highly constrained warehouse layouts is a challenging task for layout planners. Those experts create feasible layouts analytically based on their knowledge and experience. The presented paper proposes an AI-based approach to generate feasible warehouse layouts automatically by using answer set programming. The developed implementation is...

Probability kinematics is a leading paradigm in probabilistic belief change. It is based on the idea that conditional beliefs should be independent from changes of their antecedents’ probabilities. In this paper, we propose a re-interpretation of this paradigm for Spohn’s ranking functions which we call Generalized Ranking Kinematics as a new princ...

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...

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...

Activation-based conditional inference applies conditional reasoning to ACT-R, a cognitive architecture developed to formalize human reasoning. The idea of activation-based conditional inference is to determine a reasonable subset of a conditional belief base in order to draw inductive inferences in time. Central to activation-based conditional inf...

Delgrande's knowledge level account of forgetting provides a general approach to forgetting syntax elements from sets of formulas with links to many other forgetting operations, in particular, to Boole's variable elimination. On the other hand, marginalisation of epistemic states is a specific approach to actively reduce signatures in more complex...

The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions expressible by a total preorder over a limited set of worlds. For a belief change operator, we consider the scope,...

There are multiple ways of defining nonmonotonic inference relations based on a conditional knowledge base. While the axiomatic system P is an important standard for such plausible nonmonotonic reasoning, inference relations obtained from system Z or from c-representations have been designed which go beyond system P by selecting preferred models fo...

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...

An important concept for nonmonotonic reasoning in the context of a conditional belief base \(\mathcal R\) is syntax splitting, essentially stating that taking only the syntactically relevant part of \(\mathcal R\) into account should be sufficient. In this paper, for the semantics of ordinal conditional functions (OCF) of \(\mathcal R\), we introd...

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 bring in the concept of focused inference into the field of qualitative nonmonotonic reasoning by applying focused inference to System P. The idea behind drawing focused inferences is to concentrate on knowledge which seems to be relevant for answering a query while completely disregarding the remaining knowledge even at the risk of missing some...

Descriptor revision is a belief change framework that was introduced by Hansson as an alternative to the currently prevailing AGM paradigm. One central idea of descriptor revision is to describe the desired outcome of a belief change. Thus, descriptor revision allows expressing different kinds of belief change operations like revision or contractio...

For characterizing belief sets consisting of independent parts, Parikh introduced the notion of syntax splitting. Corresponding postulates have been developed for the reasoning from and for the revision of belief bases with respect to syntax splitting. Kern-Isberner and Brewka introduced syntax splitting for epistemic states and iterated belief rev...

Given a belief base ∆ consisting of a set of conditionals,there are many different ways an agent may inductivelycomplete the knowledge represented by ∆ to a completeepistemic state; two well-known approaches are given by systemP and system Z, and also each ranking model of ∆ induces afull inference relation. C-representations are special rankingmod...

In non-monotonic reasoning, conditional belief bases mostly contain positive information in the form of standard conditionals. However, in practice we are often confronted with negative information, stating that a conditional does \emph{not} hold, i.e. we need a suitable approach for reasoning over belief bases $\Delta$ with positive and negative i...

In belief revision theory, conditionals are often interpreted via the Ramsey test. However, the classical Ramsey Test fails to take into account a fundamental feature of conditionals as used in natural language: typically, the antecedent is relevant to the consequent. Rott has extended the Ramsey Test by introducing so-called difference-making cond...

In belief revision theory, conditionals are often interpreted via the Ramsey test. However, the classical Ramsey Test fails to take into account a fundamental feature of conditionals as used in natural language: typically, the antecedent is relevant to the consequent. Rott has extended the Ramsey Test by introducing so-called difference-making cond...

According to Boutillier, Darwiche and Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction, a similar formulation is not known. In particular, the characterisation for revision does not immediately yield a characterisation for contraction, because in the se...

Parikh developed the notion of syntax splitting to describe belief sets with independent parts. He also formulated a postulate demanding that belief revisions respect syntax splittings in belief sets. The concept of syntax splitting was later transferred to epistemic states with total preorders and ranking functions by Kern-Isberner and Brewka alon...

Syntax splitting, first introduced by Parikh in 1999, is a natural and desirable property of KR systems. Syntax splitting combines two aspects: it requires that the outcome of a certain epistemic operation should only depend on relevant parts of the underlying knowledge base, where relevance is given a syntactic interpretation (relevance). It also...

According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction a similar formulation is not known. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identit...

The first reference on rationality that integrates accounts from psychology and philosophy, covering descriptive and normative theories from both disciplines. Both analytic philosophy and cognitive psychology have made dramatic advances in understanding rationality, but there has been little interaction between the disciplines. This volume offers t...

Understanding, formalizing and modelling human reasoning is a core topic of artificial intelligence. In psychology, numerous fallacies and paradoxes have shown that classical logic is not a suitable logical framework for this. In a recent paper, Eichhorn, Kern-Isberner, and Ragni have succeeded in resolving paradoxes and modelling human reasoning c...

In diesem Kapitel werden wir auf die Grundlagen logikbasierter Ansätze zur Wissensrepräsentation und -inferenz eingehen. Neben einem allgemeinen Überblick werden wir dabei insbesondere die charakteristischen Eigenschaften klassisch-logischer Systeme herausarbeiten, die zum einen den Kern vieler Repräsentationssprachen bilden und zum anderen als Ref...

Mit den regelbasierten Systemen haben wir eine wichtige Grundform wissensbasierter Systeme kennengelernt. Ihre Bedeutung verdanken sie nicht zuletzt dem Umstand, dass Regeln in besonderem Maße als Repräsentanten von Wissen akzeptiert und geschätzt werden. Regeln drücken generisches Wissen aus, also allgemeines, vom speziellen Kontext abstrahierende...

Neben den symbolischenMethoden zur Repräsentation unsicheren Wissens verfolgte man von Anfang an auch quantitative Ansätze zur Repräsentation und Verarbeitung von Wissen. Ein wegweisendes Beispiel hierfür war MYCIN, eines der ersten namhaften Expertensysteme (siehe Kapitel 4.7). Im Allgemeinen werden dabei den Aussagen bzw. Formeln numerische Größe...

In Kapitel 2 haben wir bereits ein regelbasiertes System kennengelernt: den Geldautomaten. Wir führten einige Regeln an, die die Bewilligung einer Auszahlung gestatten oder verweigern. Damit der Geldautomat korrekt arbeitet, muss ein Regelinterpreter die Anwendung der Regeln steuern.

Wie das Ziehen von Schlussfolgerungen und das Lernen ist das zielgerichtete Planen etwas, in dem sich intelligentes Verhalten in besonderer Weise manifestiert. Während es aber beim Schließen darum geht festzustellen, ob ein bestimmter Sachverhalt vorliegt oder nicht, ist das Ziel des Planens ein anderes. Gegeben sei ein vorliegender Zustand und die...

Kaum ein anderes Paradigma hat die Entwicklung der Künstlichen Intelligenz in den letzten Jahren so beeinflusst und vorangetrieben wie das Konzept des Agenten. Ein Agent ist letztendlich das Zielobjekt, in dem alle Forschungsrichtungen der KI zusammenlaufen und zu einem integrierten, in seine Umgebung eingebetteten und mit ihr kommunizierenden Syst...

Nach ersten Beispielen für wissensbasierte Systeme gehen wir auf die Unterscheidung zwischen Expertensystemen und wissensbasierten Systemen ein. Angaben zu der Geschichte des Gebietes werden ergänzt durch die Vorstellung des für die Geschichte so wichtigen medizinischen Expertensystems MYCIN. Danach beschreiben wir den generellen Aufbau eines wisse...

Der Bereich der Argumentation hat eine lange Tradition. Historisch gesehen ist Argumentation eine Teildisziplin der Philosophie, die sich mit der Analyse von Diskursen und mit Rhetorik beschäftigt. Dabei wird Argumentation zur dialektischen Erörterung benutzt, in der ein Sachverhalt unter unterschiedlichen Gesichtspunkten beleuchtet wird.

Ein Nachteil des üblichen probabilistischen Ansatzes ist die Erfordernis präziser Wahrscheinlichkeitswerte. Zum einen ist oft die Spezifikation solcher exakten Werte problematisch, zum anderen lässt sich probabilistische Unsicherheit nicht von der durch fehlendes Wissen bedingten Unsicherheit unterscheiden. Werfen wir eine Münze, so schätzen wir di...

Ähnlich wie es grundlegende Schwierigkeiten gibt, den Begriff der künstlichen Intelligenz exakt zu definieren, gilt dies auch für den Begriff des maschinellen Lernens. Beide Begriffe stehen nämlich in einem ähnlichen Verhältnis zueinander, wie dies auch die Begriffe der Intelligenz und des Lernens tun. Intelligentes Verhalten wird oft eng mit der F...

Während bei Truth Maintenance-Systemen die nichtmonotone Ableitung im Vordergrund steht und nichtmonotone Regeln hier – eher unscheinbar – als ein Mittel zum Zweck eingesetzt werden, rücken diese unsicheren Regeln (defeasible rules) in der Default-Logik in den Mittelpunkt des Geschehens. Sie bekommen einen eigenen Namen, Default-Regel oder einfach...

Schon der Name “Nichtmonotone Logik(en)” mag Unbehagen einflößen. Man ist froh, endlich die formalen Hürden klassischer Logik genommen zu haben, hat ihre Formalismen verinnerlicht und weiß vielleicht sogar ihre Klarheit und verlässliche Stärke zu schätzen – wozu sich also nun mit einem Thema beschäftigen, das wie eine abstruse und höchst artifiziel...

Kein anderes Gebiet im gesamten Bereich der Deduktions- und Inferenzsysteme ist so erfolgreich in praktische Anwendungen vorgedrungen wie das logische Programmieren. Beim klassischen logischen Programmieren handelt es sich um einen normalen Resolutionskalkül mit einer syntaktisch sehr einfach zu charakterisierenden Restriktion: Es werden nur Hornkl...

The probabilistic Description Logic is an extension of the Description Logic that allows for uncertain conditional statements of the form “if C holds, then D holds with probability p,” together with probabilistic assertions about individuals. In , probabilities are understood as an agent’s degree of belief. Probabilistic conditionals are formally i...

Intentional forgetting means to deliberately give up information and is a crucial part of change or consolidation processes, or to make knowledge more compact. Two well-known forgetting operations are contraction in the AGM theory of belief change, and various types of variable elimination in logic programming. While previous work dealt with postul...

The probabilistic Description Logic extends the classical Description Logic with probabilistic conditionals of the form (D|C)[p] stating that “D follows from C with probability p.” Conditionals are interpreted based on the aggregating semantics where probabilities are understood as degrees of belief. For reasoning with probabilistic conditional kno...

Autonomous vehicles for in-plant transportation are widely accepted in the industry nowadays. If applied in order picking, efficiency of their operations is essential for the performance of the overall system. Even though the developed systems are tailored to work in highly volatile environments their procedures are programmed in a comparably old-f...

We present \(\mathcal {ALC}^\mathsf {ME}\), a probabilistic variant of the Description Logic \(\mathcal {ALC}\) that allows for representing and processing conditional statements of the form “if E holds, then F follows with probability p” under the principle of maximum entropy. Probabilities are understood as degrees of belief and formally interpre...

Die Darstellung und Verarbeitung jeglicher Art von Wissen – ob sicher oder unsicher, vage, unvollständig oder sogar widersprüchlich – ist in der Künstlichen Intelligenz die zentrale Aufgabe intelligenter, wissensbasierter Systeme. Den Autoren ist es gelungen, die unterschiedlichen Methoden anschaulich zu präsentieren, so dass dieses Werk zum Selbst...

This book constitutes the refereed proceedings of the 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2019, held in Belgrade, Serbia, in September 2019. The 41 full papers presented together with 3 abstracts of invited talks inn this volume were carefully reviewed and selected from 62 submissi...

While humans have developed extremely effective ways of forgetting outdated or currently irrelevant information, freeing them to process ever-increasing amounts of information, there seems to be a gap between the technically defined notions of forgetting in knowledge representation and the common-sense understanding of forgetting. In order to bring...

Forgetting is an ambivalent concept of (human) intelligence. By definition, it is negatively related to knowledge in that knowledge is lost, be it deliberately or not, and therefore, forgetting has not received as much attention in the field of knowledge representation and reasoning (KRR) as other processes with a more positive orientation, like qu...

Similarity among worlds plays a pivotal role in providing the semantics for different kinds of belief change. Although similarity is, intuitively, a context-sensitive concept, the accounts of similarity presently proposed are, by and large, context blind. We propose an account of similarity that is context sensitive, and when belief change is conce...

Current trends, like digital transformation and ubiquitous computing, yield in massive increase in available data and information. In artificial intelligence (AI) systems, capacity of knowledge bases is limited due to computational complexity of many inference algorithms. Consequently, continuously sampling information and unfiltered storing in kno...

While the axiomatic system P is an important standard for plausible, nonmonotonic inferences from conditional knowledge bases, it is known to be too weak to solve benchmark problems like Irrelevance or Subclass Inheritance. Ordinal conditional functions provide a semantic base for system P and have often been used to design stronger inference relat...

Conditional information is an integral part of representation and inference processes of causal relationships, temporal events, and even the deliberation about impossible scenarios of cognitive agents. For formalizing these inferences, a proper formal representation is needed. Psychological studies indicate that classical, monotonic logic is not th...

Probabilistic reasoning under the principle of maximum entropy (so-called MaxEnt principle) is a viable and convenient alternative to graph-based methodologies such as Bayesian networks that realises an idea of information economy, i.e., of being as unbiased as possible. For relational conditional knowledge, the aggregating semantics provides a sem...

By using the concept of possible worlds as system states, it is possible to express a system’s internal state with the configuration of the system’s variables. In the same way, the (usually incomplete and not necessarily correct) belief of an intelligent agent about the system’s state can be expressed by a set of possible worlds. If this belief is...

First-order typed model counting extends first-order model counting by the ability to distinguish between different types of models. In this paper, we exploit this benefit in order to calculate weighted conditional impacts (WCIs) which play a central role in nonmonotonic reasoning based on conditionals. More precisely, WCIs store information about...

A propositional conditional of the form , representing the default rule “If A, then usually B”, goes beyond the limits of classical logic, and the semantics of a knowledge base consisting of such conditionals must take into account the three-valued nature of conditionals. Ordinal conditional functions (OCF), also called ranking functions, assign a...

Ranking functions constitute a powerful formalism for nonmonotonic reasoning based on qualitative conditional knowledge. Conditionals are formalized defeasible rules and thus allow one to express that certain individuals or subclasses of some broader concept behave differently. More precisely, in order to model these exceptions by means of ranking...

Conditional knowledge bases consisting of sets of conditionals are used in inductive nonmonotonic reasoning and can represent the defeasible background knowledge of a reasoning agent. For the comparison of the knowledge of different agents, as well as of different approaches to nonmonotonic reasoning, it is beneficial if these knowledge bases are a...

Background knowledge is often represented by sets of conditionals of the form “if A then usually B”. Such knowledge bases should not be circuitous, but compact and easy to compare in order to allow for efficient processing in approaches dealing with and inferring from background knowledge, such as nonmonotonic reasoning. In this paper we present tr...

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence a...

This book constitutes the refereed proceedings of the 40th Annual German Conference on Artificial Intelligence, KI 2017 held in Dortmund, Germany in September 2017. The 20 revised full technical papers presented together with 16 short technical communications were carefully reviewed and selected from 73 submissions. The conference cover a range of...

The number of parameters leading to a defined medical cancer therapy is growing rapidly. A clinical decision support system intended for better managing the resulting complexity must be able to reason about the respective active ingredients and their interrelationships. In this paper, we present a corresponding ontology and illustrate its use for a...