Stratified Labelings for Abstract Argumentation

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions

Characterizing the principle of minimum cross-entropy within a conditional-logical framework

AbstractThe principle of minimum cross-entropy (ME-principle) is often used as an elegant and powerful tool to build up complete probability distributions when only partial knowledge is available. The inputs it may be applied to are a prior distribution P and some new information R, and it yields as a result the one distribution P∗ that satisfies R and is closest to P in an information-theoretic sense. More generally, it provides a “best” solution to the problem “How to adjust P to R?”In this paper, we show how probabilistic conditionals allow a new and constructive approach to this important principle. Though popular and widely used for knowledge representation, conditionals quantified by probabilities are not easily dealt with. We develop four principles that describe their handling in a reasonable and consistent way, taking into consideration the conditional-logical as well as the numerical and probabilistic aspects. Finally, the ME-principle turns out to be the only method for adjusting a prior distribution to new conditional information that obeys all these principles.Thus a characterization of the ME-principle within a conditional-logical framework is achieved, and its implicit logical mechanisms are revealed clearly

On the Modelling of an Agent's Epistemic State and its Dynamic Changes

Given a set of unquantified conditionals considered as default rules or a set of quantified conditionals such as probabilistic rules, an agent can build up its internal epistemic state from such a knowledge base by inductive reasoning techniques. Besides certain (logical) knowledge, epistemic states are supposed to allow the representation of preferences, beliefs, assumptions etc. of an intelligent agent. If the agent lives in a dynamic environment, it has to adapt its epistemic state constantly to changes in the surrounding world in order to be able to react adequately to new demands. In this paper, we present a high-level specification of the Condor system that provides powerful methods and tools for managing knowledge represented by conditionals and the corresponding epistemic states of an agent. Thereby, we are able to elaborate and formalize crucial interdependencies between different aspects of knowledge representation, knowledge discovery, and belief revision. Moreover, this specification, using Gurevich's Abstract State Machines, provides the basis for a stepwise refinement development process of the Condor system based on the ASM methodology

Modelling and Implementing a Knowledge Base for Checking Medical Invoices with DLV

Checking medical invoices, done by every health insurance company, is a labor-intensive task. Both speed and quality of executing this task may be increased by the knowledge-based decision support system ACMI which we present in this paper. As the relevant regulations also contain various default rules, ACMI`s knowledge core is modelled using the answer set programming paradigm. It turned out that all relevant rules could be expressed directly in this framework, providing for a declarative and easily extendable and modifiable knowledge base. ACMI is implemented using the DLV system

Ranking Theory

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology

Inductive Reasoning With Difference-Making Conditionals

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 conditionals that encode a notion of relevance. This paper explores difference-making conditionals in the framework of Spohn’s ranking functions. We show that they can be expressed by standard conditionals together with might conditionals. We prove that this reformulation is fully compatible with the logic of difference-making conditionals, as introduced by Rott. Moreover, using c-representations, we propose a method for inductive reasoning with sets of difference-making conditionals and also provide a method for revising ranking functions by a set of difference-making conditionals