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

Extending the Harper Identity to Iterated Belief Change

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators

An Investigation of Darwiche and Pearl's Postulates for Iterated Belief Update

Belief revision and update, two significant types of belief change, both focus on how an agent modify her beliefs in presence of new information. The most striking difference between them is that the former studies the change of beliefs in a static world while the latter concentrates on a dynamically-changing world. The famous AGM and KM postulates were proposed to capture rational belief revision and update, respectively. However, both of them are too permissive to exclude some unreasonable changes in the iteration. In response to this weakness, the DP postulates and its extensions for iterated belief revision were presented. Furthermore, Rodrigues integrated these postulates in belief update. Unfortunately, his approach does not meet the basic requirement of iterated belief update. This paper is intended to solve this problem of Rodrigues's approach. Firstly, we present a modification of the original KM postulates based on belief states. Subsequently, we migrate several well-known postulates for iterated belief revision to iterated belief update. Moreover, we provide the exact semantic characterizations based on partial preorders for each of the proposed postulates. Finally, we analyze the compatibility between the above iterated postulates and the KM postulates for belief update

From iterated revision to iterated contraction: extending the Harper Identity

The study of iterated belief change has principally focused on revision, with the other main operator of AGM belief change theory, namely contraction, receiving comparatively little attention. In this paper we show how principles of iterated revision can be carried over to iterated contraction by generalising a principle known as the ‘Harper Identity’. The Harper Identity provides a recipe for defining the belief set resulting from contraction by a sentence A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A. Here, we look at ways to similarly define the conditional belief set resulting from contraction by A. After noting that the most straightforward proposal of this kind leads to triviality, we characterise a promising family of alternative suggestions that avoid such a result. One member of that family, which involves the operation of rational closure, is noted to be particularly theoretically fruitful and normatively appealing

Control room agents : an information-theoretic approach

In this thesis, a particular class of agent is singled out for examination. In order to provide a guiding metaphor, we speak of control room agents. Our focus is on rational decision- making by such agents, where the circumstances obtaining are such that rationality is bounded. Control room agents, whether human or non-human, need to reason and act in a changing environment with only limited information available to them. Determining the current state of the environment is a central concern for control room agents if they are to reason and act sensibly. A control room agent cannot plan its actions without having an internal representation (epistemic state) of its environment, and cannot make rational decisions unless this representation, to some level of accuracy, reflects the state of its environment. The focus of this thesis is on three aspects regarding the epistemic functioning of a control room agent: 1. How should the epistemic state of a control room agent be represented in order to facilitate logical analysis? 2. How should a control room agent change its epistemic state upon receiving new information? 3. How should a control room agent combine available information from different sources? In describing the class of control room agents as first-order intentional systems hav- ing both informational and motivational attitudes, an agent-oriented view is adopted. The central construct used in the information-theoretic approach, which is qualitative in nature, is the concept of a templated ordering. Representing the epistemic state of a control room agent by a (special form of) tem- plated ordering signals a departure from the many approaches in which only the beliefs of an agent are represented. Templated orderings allow for the representation of both knowledge and belief. A control room agent changes its epistemic state according to a proposed epistemic change algorithm, which allows the agent to select between two well-established forms of belief change operations, namely, belief revision and belief update. The combination of (possibly conflicting) information from different sources has re- ceived a lot of attention in recent years. Using templated orderings for the semantic representation of information, a new family of purely qualitative merging operations is developed.School of ComputingPh. D. (Computer Science