Instructors

• Richard Booth (Cardiff University, UK)

• Jake Chandler (La Trobe University, Melbourne, Australia)

Description

Formal ontologies provide a specification of the conceptualisation of a given domain for the purposes of knowledge and data management and play a prominent role in the so-called Semantic Web. Among the main formalisms involved in representing ontologies are description logics (DL’s). These typically decidable fragments of first order logic offer a convenient balance between expressivity and complexity and their study is the focus of a thriving research community.

Over the past few decades, it has been increasingly recognised that provisions need to be made for the amendment of existing ontologies in response to new considerations. Such amendments include most notably the tasks of (1) revising ontologies so as to incorporate new information, (2) debugging inconsistent or incoherent ontologies by weakening their sets of axioms and (3) merging possibly conflicting ontologies over a given domain.

Those with a broad background in KR will no doubt be familiar with the existence of a well-established set of axiomatic models that could be put to work in rigorously addressing these issues. The field of belief revision, closely connected to that of nonmonotonic reasoning, studies various procedures for adjusting the corpus of beliefs of an agent in response to the addition or deletion of one of its members. Similarly, an outgrowth of the economic subdiscipline of social choice known as judgment aggregation considers methods for aggregating, into a group-level verdict, the views of a set of possibly disagreeing agents.

Unfortunately, however, much of the work in these fields has assumed an underlying logic that exhibits a number of features of propositional logic, including the likes of closure under negation or again so-called “decomposability”, which are not shared by some of the more lightweight DL’s popular in the field of ontology. As a result, a series of papers published over the past 20 years has explored various manners in which traditional belief revision and merging frameworks might be adapted to the ontological context.

In this tutorial, after providing a systematic introduction to belief revision, judgment aggregation and description logics, we offer a survey of these developments and some of the open questions that remain.

Outline of the Tutorial

1. Introduction

2. Belief revision in propositional logic

3. Judgment aggregation in propositional logic

4. Ontologies and description logics

5. Belief revision and judgment aggregation in description logics

6. Recap and open problems

Target Audience and Prerequisites

• This tutorial is pitched at an extremely introductory level. It aims to familiarise researchers working in a proper subset of the fields of belief revision, judgment aggregation and ontology with elementary notions, key results and recent developments in the remaining fields.

• Prerequisite knowledge:

• Basic notions of propositional and predicate logic

• Passing familiarity with one of more of the following areas useful but not essential: belief revision, judgment aggregation, description logics.

Suggested Reading

• G. Pigozzi (2021). Belief Merging and Judgment Aggregation. In The Stanford Encyclopedia of Philosophy (Spring 2021 Edition), Edward N. Zalta (ed.)

• P. Peppas (2008). Belief Revision. In Handbook of Knowledge Representation, F. van Harmelen, V. Lifschitz and B. Porter (Eds.).

• F. Baader, I. Horrocks and U. Sattler (2008). Description Logics. In Handbook of Knowledge Representation, F. van Harmelen, V. Lifschitz and B. Porter (Eds.).

Slides

To appear here nearer to the tutorial.