Belief Change: From 1985 to present days

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases.

In this tutorial, the first 35 years of this development are summarized.

The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, and criticism of the model.


PDF format.

A detailed outline of the tutorial

1 Introduction
2 Equivalent characterizations
2.1 AGM briefly summarized
2.2 Safe and kernel contraction
2.3 Epistemic Entrenchment
2.4 Grove’s spheres
2.5 Distance models
2.6 Specified meet contraction
3 Criticism of the model
3.1 The recovery postulate
3.2 The success postulates
3.3 Are belief sets too large?
3.4 Lack of information in the belief set
4 Extended representations of belief states
4.1 Belief bases
4.2 Probability and plausibility
4.3 Ranking models
4.4 Extensions of the language
4.5 Change in norms, preferences, goals, and desires
5 Iterated change
5.1 Revising epistemic states
5.2 Major classes of iterable operators
6 Alternative operators of change
6.1 Update
6.2 Non-prioritized change
6.3 Changes in the strength of beliefs
6.4 Resource-bounded change and inconsistency management
6.5 Multiple change
6.6 Indeterministic change
6.7 Some other operators of change
7 Applications and connections
7.1 Non-monotonic and defeasible logic
7.2 Description logic
7.3 Horn clause contraction functions
7.4 Game theory
7.5 Argumentation
7.6 Modal and dynamic logics
7.7 Belief Change by translation between logics
7.8 Truth
7.9 Use of choice functions and related preference orderings
8 Computability and implementation

The tutorial can be summarized in the following two figures:

Potential target audience

The tutorial is intended for a wide audiences. The main area of the course is “Knowledge Representation, Reasoning and Logic”. However it is also interesting for the people in the following areas:

Agent-based and Multi-agent Systems
Machine Learning
Robotics and Vision (in particular Cognitive Robotics)
Multidisciplinary Topics And Applications
Uncertainty in AI
Web and Knowledge-based Information Systems

The prerequisite it is basic knowledge of logic and a background in AI, in particular Knowledge Representation and Reasoning.


Eduardo Fermé
Faculty of Exact Sciences and Engineering
University of Madeira
Campus Universitário da Penteada 9000-390 Funchal, Madeira, Portugal.

Brief Biography

Eduardo Fermé made in 2008 the Aggregation in Informatics Engineering in the University of Madeira.
He completed in 1999 a PhD in Computer Science by the University of Buenos Aires, Argentina and in 2011 a PhD in Philosophy by the Kungliga Tekniska Högskolan (KTH), Sweden .
Since 2004 is Associate Professor in the University of Madeira. Since 2013 is integrated Member of NOVA LINCS (FCT centre, New University of Lisbon). Since 2020 Coordinator of the Pole of NOVA-LINCS at University of Madeira.
He supervised 3 PhD thesis and actually supervises other 3. He supervised 27 MSc dissertations and co-supervised 1 and actually supervises 1. He published 1 books in Springer Briefs in Computer Science Series, edited 5 books and published 11 book chapters, 26 Journal papers. (18 Q1, 2 Q2, 1 Q3, 4 Q4) and more than 40 Conference papers (among them, 12 in A* or A conferences). He was Invited Editor in 3 journals.
In their professional activities interacted with 80 collaborator(s) co-authorship of scientific papers.
He is member of the Editorial Board of the Journal of Applied Logics (College Publications), CAAI Transactions on Intelligence Technology. Sponsored by the Chinese Association for Artificial Intelligence (CAAI) and Editorial Board member of Inteligencia Artificial. Iberoamerican Journal of Artificial Intelligence. Edited by Iberamia.
Eduardo Fermé has working from 1988 in the area of Knowledge Representation and Reasoning – Non Monotonic Reasoning - Belief Revision.

Orcid CV

Background in the area of the tutorial

Eduardo Fermé worked in belief revision from 1988 (He started hes degree thesis under the advise of Carlos Alchourrón). he has published in the area: A survey book, two edited books and more than 50 papers and he was one of the editors of the special issue of the 25 years of the AGM, published in the Journal of Philosophical Logic. (http://www.springerlink.com/content/0022-3611/40/2/)