Precise Propagation of Upper and Lower Probability Bounds in System P

In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony of System P+ proposed by Adams in his extended probability logic.Comment: 8 pages -8th Intl. Workshop on Non-Monotonic Reasoning NMR'2000, April 9-11, Breckenridge, Colorad

Supporting case-based retrieval by similarity skylines: Basic concepts and extensions

Conventional approaches to similarity search and case-based retrieval, such as nearest neighbor search, require the speci cation of a global similarity measure which is typically expressed as an aggregation of local measures pertaining to di erent aspects of a case. Since the proper aggregation of local measures is often quite di cult, we propose a novel concept called similarity skyline. Roughly speaking, the similarity skyline of a case base is de ned by the subset of cases that are most similar to a given query in a Pareto sense. Thus, the idea is to proceed from a d-dimensional comparison between cases in terms of d (local) distance measures and to identify those cases that are maximally similar in the sense of the Pareto dominance relation [2]. To re ne the retrieval result, we propose a method for computing maximally diverse subsets of a similarity skyline. Moreover, we propose a generalization of similarity skylines which is able to deal with uncertain data described in terms of interval or fuzzy attribute values. The method is applied to similarity search over uncertain archaeological data

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