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Collaborating Authors

Beierle, Christoph


Inference with System W Satisfies Syntax Splitting

arXiv.org Artificial Intelligence

In this paper, we investigate inductive inference with system W from conditional belief bases with respect to syntax splitting. The concept of syntax splitting for inductive inference states that inferences about independent parts of the signature should not affect each other. This was captured in work by Kern-Isberner, Beierle, and Brewka in the form of postulates for inductive inference operators expressing syntax splitting as a combination of relevance and independence; it was also shown that c-inference fulfils syntax splitting, while system P inference and system Z both fail to satisfy it. System W is a recently introduced inference system for nonmonotonic reasoning that captures and properly extends system Z as well as c-inference. We show that system W fulfils the syntax splitting postulates for inductive inference operators by showing that it satisfies the required properties of relevance and independence. This makes system W another inference operator besides c-inference that fully complies with syntax splitting, while in contrast to c-inference, also extending rational closure.


A Conditional Perspective on the Logic of Iterated Belief Contraction

arXiv.org Artificial Intelligence

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 characterization theorems and provide formulations by postulates which highlight how the change of beliefs and of conditional beliefs is constrained, whenever that is possible. The first group is similar to the syntactic Darwiche-Pearl postulates. As a second group, we consider semantic postulates for iteration of contraction by Chopra, Ghose, Meyer and Wong, and by Konieczny and Pino P\'erez, respectively, and we provide novel syntactic counterparts. Third, we propose a contraction analogue of the independence condition by Jin and Thielscher. For the fourth group, we consider natural and moderate contraction by Nayak. Methodically, we make use of conditionals for contractions, so-called contractionals and furthermore, we propose and employ the novel notion of $ \alpha $-equivalence for formulating some of the new postulates.


Conditional Inference and Activation of Knowledge Entities in ACT-R

arXiv.org Artificial Intelligence

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 inference is the activation function which assigns to the conditionals in the belief base a degree of activation mainly based on the conditional's relevance for the current query and its usage history.


On Limited Non-Prioritised Belief Revision Operators with Dynamic Scope

arXiv.org Artificial Intelligence

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, which consists of those beliefs which yield success of revision. We show that for each set satisfying single sentence closure and disjunction completeness there exists a dynamic-limited revision having the union of this set with the beliefs set as scope. We investigate iteration postulates for belief and scope dynamics and characterise them for dynamic-limited revision. As an application, we employ dynamic-limited revision to studying belief revision in the context of so-called inherent beliefs, which are beliefs globally accepted by the agent. This leads to revision operators which we call inherence-limited. We present a representation theorem for inherence-limited revision, and we compare these operators and dynamic-limited revision with the closely related credible-limited revision operators.


Using Finite-State Machines to Automatically Scan Classical Greek Hexameter

arXiv.org Artificial Intelligence

Greek literature has, for centuries, served as a paradigm and model for literary writing all over Europe. The oldest surviving texts of Classical Greek literature - texts such as the Iliad, the Odyssey, and the works of Hesiod - are epic poems that all share the same metre: hexameter. They are written in an artificial language that has never been spoken in everyday life and owes its origin and many of its peculiarities to the nature of metrically bound language (Meister (1921)). Comprehensive hexameter annotation is, therefore, crucial for large-scale and data-driven investigations into some of the linguistic features of Ancient Greek epic language. Furthermore, it may provide additional criteria for the evaluation of Homer's repeated verses, the so-called iterata. Within Classical Philology, controversy around the nature of the Homeric repetitions started in 1840, and it remained one of the central research questions in the field for a long period of time (see Strasser (1984), pp.


Descriptor Revision for Conditionals: Literal Descriptors and Conditional Preservation

arXiv.org Artificial Intelligence

Descriptor revision by Hansson is a framework for addressing the problem of belief change. In descriptor revision, different kinds of change processes are dealt with in a joint framework. Individual change requirements are qualified by specific success conditions expressed by a belief descriptor, and belief descriptors can be combined by logical connectives. This is in contrast to the currently dominating AGM paradigm shaped by Alchourr\'on, G\"ardenfors, and Makinson, where different kinds of changes, like a revision or a contraction, are dealt with separately. In this article, we investigate the realisation of descriptor revision for a conditional logic while restricting descriptors to the conjunction of literal descriptors. We apply the principle of conditional preservation developed by Kern-Isberner to descriptor revision for conditionals, show how descriptor revision for conditionals under these restrictions can be characterised by a constraint satisfaction problem, and implement it using constraint logic programming. Since our conditional logic subsumes propositional logic, our approach also realises descriptor revision for propositional logic.


Nonmonotonic Inferences with Qualitative Conditionals based on Preferred Structures on Worlds

arXiv.org Artificial Intelligence

A conditional knowledge base R is a set of conditionals of the form "If A, the usually B". Using structural information derived from the conditionals in R, we introduce the preferred structure relation on worlds. The preferred structure relation is the core ingredient of a new inference relation called system W inference that inductively completes the knowledge given explicitly in R. We show that system W exhibits desirable inference properties like satisfying system P and avoiding, in contrast to e.g. system Z, the drowning problem. It fully captures and strictly extends both system Z and skeptical c-inference. In contrast to skeptical c-inference, it does not require to solve a complex constraint satisfaction problem, but is as tractable as system Z.


Transforming Conditional Knowledge Bases into Renaming Normal Form

AAAI Conferences

While for classical logics, the motto ``Truth is invariant under the change of notation'' has been studied extensively, less attention has been paid to this aspect in defeasible logics. In this paper, we address equivalences and transformations among conditional knowledge bases that take renamings of the underlying signature into account. Extending previous proposals, we introduce the concepts of \emph{renaming normal form} and \emph{renaming antecedent normal form} for arbitrary knowledge bases and across different signatures. We present procedures to transform every knowledge base to corresponding, up to propositional normalization uniquely determined normal forms and study their properties. Using the obtained normal forms allows for systematically identifying equivalences among knowledge bases, for easier and more transparent comparisons, and for simplified descriptions of algorithms operating on knowledge bases by avoiding tedious, but uninteresting borderline cases.


A Conditional Perspective for Iterated Belief Contraction

arXiv.org Artificial Intelligence

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. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do not transfer easily between iterated revision and contraction. In this article, we develop an axiomatisation of iterated contraction in terms of changing conditional beliefs. We prove that the new set of postulates conforms semantically to the class of operators like the ones given by Konieczny and Pino Pérez for iterated contraction. 1 Introduction For the three main classes of theory change, revision, expansion and contraction, different characterisations are known [12], which are heavily supported by the correspondence between revision and contraction via the Levi and Harper identities [13, 17].


Decrement Operators in Belief Change

arXiv.org Artificial Intelligence

While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for each of them a representation theorem in the framework of total preorders is given. Furthermore, we present two types of decrement operators which have a unique representative.