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Kern-Isberner, Gabriele


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.


On the Correspondence between Abstract Dialectical Frameworks and Nonmonotonic Conditional Logics

AAAI Conferences

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 first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations.


Generalized Ranking Kinematics for Iterated Belief Revision

AAAI Conferences

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 principle for iterated belief revision of ranking functions by sets of conditional beliefs. This general setting also covers iterated revision by propositional beliefs. We then present c-revisions as belief change methodology that satisfies Generalized Ranking Kinematics.


Context-Based Inferences from Probabilistic Conditionals with Default Negation at Maximum Entropy

AAAI Conferences

The principle of maximum entropy (MaxEnt) constitutes a powerful formalism for nonmonotonic reasoning based on probabilistic conditionals. Conditionals are defeasible rules which allow one to express that certain subclasses of some broader concept behave exceptional. In the (common) probabilistic semantics of conditional statements, these exceptions are formalized only implicitly: The conditional (B|A)[p] expresses that if A holds, then B is typically true, namely with probability p, but without explicitly talking about the subclass of A for which B does not hold. There is no possibility to express within the conditional that a subclass C of A is excluded from the inference to B because one is unaware of the probability of B given C. In this paper, we apply the concept of default negation to probabilistic MaxEnt reasoning in order to formalize this kind of unawareness and propose a context-based inference formalism. We exemplify the usefulness of this inference relation, and show that it satisfies basic formal properties of probabilistic reasoning.


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].


Integrating Typed Model Counting into First-Order Maximum Entropy Computations and the Connection to Markov Logic Networks

AAAI Conferences

The principle of maximum entropy (MaxEnt) provides a well-founded methodology for commonsense reasoning based on probabilistic conditional knowledge. We show how to calculate MaxEnt distributions in a first-order setting by using typed model counting and condensed iterative scaling. Further, we discuss the connection to Markov Logic Networks for drawing inferences.


Axiomatic Evaluation of Epistemic Forgetting Operators

AAAI Conferences

Forgetting as a knowledge management operation has received much less attention than operations like inference, or revision. It was mainly in the area of logic programming that techniques and axiomatic properties have been studied systematically. However, at least from a cognitive view, forgetting plays an important role in restructuring and reorganizing a human's mind, and it is closely related to notions like relevance and independence which are crucial to knowledge representation and reasoning. In this paper, we propose axiomatic properties of (intentional) forgetting for general epistemic frameworks which are inspired by those for logic programming, and we evaluate various forgetting operations which have been proposed recently by Beierle et al. according to them. The general aim of this paper is to advance formal studies of (intentional) forgetting operators while capturing the many facets of forgetting in a unifying framework in which different forgetting operators can be contrasted and distinguished by means of formal properties.


Decision Support Core System for Cancer Therapies Using ASP-HEX

AAAI Conferences

MAMMA-DSCS (mammary carcinoma decision support core system) is a prototype implementation designed for the support of decision processes for breast cancer (mammary carcinoma) treatment plans: Given a set of patient values, the system suggests different applicable treatment plans. As additional knowledge sources, MAMMA-DSCS uses external ontologies containing further information and correlations which are not directly tied to the tumor itself (e.g. toxicities, drug interactions). As a consequence, general knowledge like the substance composition of a specific therapy and its pharmacological hierarchy, can be separated from the knowledge about the applicability of therapies for a patient. The latter is encoded in an ASP program that is able to access the external ontologies and to take the obtained information into account for determining the set of all therapy plans that may be applied in a given situation. The ASP program models medical knowledge combining general guidelines and up-to-date expert knowledge for treating breast cancer on a very finegrained level, originating from a hospital in Germany.