Decrement Operators in Belief Change

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 sub-types of decrement operators

Algebras of Measurements: the logical structure of Quantum Mechanics

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.Comment: Submitted, 30 page

Expressing Belief Flow in Assertion Networks

Abstract. In the line of some earlier work done on belief dynamics, we propose an abstract model of belief propagation on a graph based on the methodology of the revision theory of truth. A modal language is developed for portraying the behavior of this model, and its expressiveness is discussed. We compare the proposal of this model as well as the language developed with some of the existing frameworks for modelling communication situations.

Logics of knowledge and action: critical analysis and challenges

International audienceWe overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges

Handling Sequences of Belief Change in a Multi-Agent Context

This paper focuses on the features of belief change in a multiagent context. Agents have to consider information received from the other agents and the ability of how to change beliefs after receiving a message is a prerequisite for many multi-agents problems. The agents are embedded in an environment where they are communicating and they have to prevent potential internal conflicts in their beliefs. We study the belief change operators in that context. Our approach is to consider that agents' belief state is a set of pairs #belief, origin of the belief# combined with a preference relation over the agents embedded in the multi-agent system. The belief revision procedure for handling received messages is a syntactic approach which aims at selecting the minimal subsets of the belief base in conflict with the received information and, according to the reliability of the sources of the conflicting beliefs, removing the less reliable beliefs in order to handle the received message. The proposed belief change operators ensure that an agent makes as few changes as possible but also handle iterated belief changes by preserving the order on the beliefs

Two Approaches to Iterated Belief Contraction

Iterated Belief Contraction is a relatively less explored area in belief change and intuition for it is often driven by work in the area of iterated belief revision. For many of the iterable belief contraction functions defined in the literature, very little is known about their properties. In this paper we recall two iterable contraction functions, Natural contraction and Priority contraction, defined by Nayak and colleagues. Here we characterize both these contraction functions via some simple properties of iterated contraction.12 page(s