Zhiqiang Zhuang

Belief Change in Nonmonotonic Multi-Context Systems

Brewka and Eiters nonmonotonic multi-context system is an elegant knowledge representation framework to model heterogeneous and nonmonotonic multiple contexts. Belief change is a central problem in knowledge representation and reasoning. In this paper we follow the classical AGM approach to investigate belief change in multi-context systems. Specifically, we formulate semantically the AGM postulates of belief expansion, revision and contraction for multi-context systems. We show that the change operations can be characterized in terms of minimal change by ordering equilibria of multi-context systems. Two distance based revision operators are obtained and related to the classical Satoh and Dalal revision operators via loop formulas.

DL-lite contraction and revision

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite. Type semantics has several advantages over the standard one. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them. Finally, the finiteness and succinctness of type semantics allow us to develop tractable algorithms for instantiating the functions.

A Unifying Framework for Probabilistic Belief Revision

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an “all purpose” method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis’s imaging. Importantly, p-revision subsumes the above three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis’ imaging all obey the basic principles of AGM revision. As well our investigation sheds light on the corresponding operation of AGM expansion in the probabilistic setting.

Syntax-Preserving Belief Change Operators for Logic Programs

Recent methods have adapted the well-established AGM and belief base frameworks for belief change to cover belief revision in logic programs. In this study here, we present two new sets of belief change operators for logic programs. They focus on preserving the explicit relationships expressed in the rules of a program, a feature that is missing in purely semantic approaches that consider programs only in their entirety. In particular, operators of the latter class fail to satisfy preservation and support, two important properties for belief change in logic programs required to ensure intuitive results. We address this shortcoming of existing approaches by introducing partial meet and ensconcement constructions for logic program belief change, which allow us to define syntax-preserving operators for satisfying preservation and support. Our work is novel in that our constructions not only preserve more information from a logic program during a change operation than existing ones, but they also facilitate natural definitions of contraction operators, the first in the field to the best of our knowledge. To evaluate the rationality of our operators, we translate the revision and contraction postulates from the AGM and belief base frameworks to the logic programming setting. We show that our operators fully comply with the belief base framework and formally state the interdefinability between our operators. We further compare our approach to two state-of-the-art logic program revision methods and demonstrate that our operators address the shortcomings of one and generalise the other method.

Three Methods for Revising Hybrid Knowledge Bases

Contemporary approaches for the Semantic Web include hybrid knowledge bases that combine ontologies with rule-based languages. Despite a number of existing combination approaches, little attention has been given to change mechanisms for hybrid knowledge bases that can appropriately handle the dynamics of information on the Web. We present here three methods for revising hybrid knowledge bases in light of new information. We show by means of representation theorems that two of them fit properly into the classic belief change framework and that each of the two generalises the third method.

Revising Possibilistic Knowledge Bases via Compatibility Degrees

Possibilistic logic is a weighted logic for dealing with incomplete and uncertain information by assigning weights to propositional formulas. A possibilistic knowledge base (KB) is a finite set of such formulas. The problem of revising a possibilistic KB by possibilistic formula is not new. However, existing approaches are limited in two ways. Firstly, they suffer from the so-called drowning effect. Secondly, they handle certain and uncertain formulas separately and most only handle certain inputs. In this paper, we propose a unified approach that caters for revision by both certain and uncertain inputs and relieves the drowning effect. The approach is based on a refined inconsistency degree function called compatibility degree which provides a unifying framework (called cd-revision) for defining specific revision operators for possibilistic KBs. Our definition leads to an algorithm for computing the result of the proposed revision. The revision operators defined in cd-revision possess some desirable properties including those from classic belief revision and some others that are specific to possibilistic revision. We also show that several major revision operators for possibilistic, stratified and prioritised KBs can be embedded in cd-revision.