Belief Revision (Computer Science)

Dual properties of the relative belief of singletons

by Fabio Cuzzolin

A study of Bayesian approximations of belief functions in the probability simplex

by Fabio Cuzzolin

Mind-reading for machines: Inferring and predicting a user's beliefs

by Richard Booth

with Alexander Nittka. Unpublished paper accompanying an invited talk at the Mahasarakham University Research Conference, Thailand, 2006

Imagine the following simple dialogue between an “intelligent” machine and a user:

User: Is Miss Thailand... more Imagine the following simple dialogue between an “intelligent” machine and a user:

User: Is Miss Thailand very beautiful? (B?)
Machine: Yes. (B)
User: Then I believe she is Miss Universe. (U )

All the machine explicitly knows from this is that (i) at the start of the dialogue, the user did not know whether B was true, and (ii) after receiving statement B the user believes U . But did the user believe U also before receiving B? Does he believe B itself after receiving it? And will he still believe B if the machine then tells him, “actually, Miss Puerto Rico is Miss Universe” (i.e., U is false!). Helping the machine find answers to questions like these is the subject of this paper. Our solution depends on the machine building a plausible model of the user and how it forms beliefs, which “best explains” the observed dialogue. Our results will be applicable in the areas of automated dialogue (e.g., chatbots) and user modelling.

On the logic of iterated non-prioritised revision

by Richard Booth

Credibility-limited revision operators in propositional logic

by Richard Booth

with Eduardo Fermé, Sébastien Konieczny and Ramon Pino Pérez, in Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012), 2012.

In Belief Revision the new information is generally accepted, following the principle of primacy of update. In some... more In Belief Revision the new information is generally accepted, following the principle of primacy of update. In some case this behavior can be criticized and one could require that some new pieces of information can be rejected by the agent because, for instance, of insufficient plausibility. This has given rise to several approaches of non-prioritized Belief Re- vision. In particular (Hansson et al. 2001) defined credibility- limited revision operators, where a revision is accepted only if the new information is a formula that belongs to a set of credible formulas. They provide several representation theo- rems in the AGM style. In this work we study credibility- limited revision operators when the information is repre- sented in propositional logic, like in the Katsuno and Mendel- zon framework. We propose a set of postulates and a repre- sentation theorem for credibility-limited revision operators. Then we explore how to generalize these definitions to the Iterated Belief Revision case, using epistemic states in the Darwiche and Pearl style.

Quantifying disagreement in argument-based reasoning

by Richard Booth

with Martin  Caminada, Mikolaj Podlaszewski and Iyad Rahwan

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an under-... more An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an under- lying logical knowledge base. This conflicting information often allows for the presence of more than one possible rea- sonable position (extension/labelling) which one can take. A relevant question, therefore, is how much these positions differ from each other. In the current paper, we will examine the issue of how to define meaningful measures of distance between the (complete) labellings of a given argumentation framework. We provide concrete distance measures based on argument-wise label difference, as well as based on the notion of critical sets, and examine their properties.

“Merely a logician's toy?” Belief revision confronting scientific theory change

by Gustavo Cevolani

On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic

by Richard Booth

with Thomas Meyer, Ivan José Varzinczak and Renata Wassermann, published in Journal of Artificial Intelligence Research, Vol. 42, pp 31-53, 2011

Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are... more Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande’s conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson’s classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a ‘hybrid’ version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

Olga Pombo & Alexander Gerner (Eds.). Abduction and the Process of Scientific Discovery. Lisbon: Publidisa, 2007

by Alexander Gerner

How serious is the paradox of serious of possibility?

by Simone Duca

Co-authored with Hannes Leitgeb, forthcoming in 'Mind'

On Revising Fuzzy Belief Bases

by Richard Booth

A method for reasoning about other agents' beliefs from observations

by Richard Booth

with Alexander Nittka, in "Texts in Logic and Games", vol. 3, 2008

How to revise a total preorder

by Richard Booth

with Thomas Meyer. In Journal of Philosophical Logic, Vol. 40(2), pp 193-238, 2011 (special commemorative issue celebrating 25 years of AGM). Combined and extended version of KR'06 and ECSQARU'07 papers.

Most approaches to iterated belief revision are accompanied by
some motivation for the use of the proposed... more Most approaches to iterated belief revision are accompanied by
some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after the first revision step. In this paper we contribute towards addressing that deficiency by providing a formal framework which goes beyond the first revision step in two ways. First, the framework is obtained by enriching the epistemic state of an agent starting from the following intuitive idea: we associate to each world x two abstract objects x+ and x−, and we assume that, in addition to preferences over the set of worlds, we are given preferences over this set of objects as well. The latter can be considered as meta-information encoded in the epistemic state which enables us to go beyond the first revision step of the revision operator being applied, and to obtain a unique set of preferences over worlds. We then extend this framework to consider, not only the revision of preferences over worlds, but also the revision of this extended structure itself. We look at some desirable properties for revising the structure and prove the consistency of these properties by giving a concrete operator satisfying all of them. Perhaps more importantly, we show that this framework has strong connections with two other types of constructions in related areas. Firstly, it can be seen as a special case of preference aggregation which opens up the possibility of extending the framework presented here into a full-fledged framework for preference aggregation and social choice theory. Secondly, it is related to existing work on the use of interval orderings in a number of different contexts.

Double preference relations for generalised belief change

by Richard Booth

Many belief change formalisms employ plausibility orderings over the set of possible worlds to determine how the... more Many belief change formalisms employ plausibility orderings over the set of possible worlds to determine how the beliefs of an agent ought to be modified after the receipt of a new epistemic input. While most such possible world semantics rely on a single order-
ing, we investigate the use of an additional preference ordering—representing, for instance, the epistemic context the agent finds itself in—to guide the process of belief change. We show that the resultant formalism provides a unifying semantics for a wide variety of belief
change operators. By varying the conditions placed on the second ordering, different families of known belief change operators can be captured, including AGM belief contraction and revision, Rott and Pagnucco’s severe withdrawal, the systematic withdrawal of Meyer et al, as well as the linear liberation and σ-liberation operators of Booth et al. Our approach also identifies novel classes of belief change operators worthy of further investigation.

Type-Theoretical Dynamics. Exploring Belief Revision in a Constructive Framework

by Giuseppe Primiero

Preprint. Final version forthcoming in "The Realism-Antirealism Debate in the Age of Alternative Logics". Springer 2011.

Oscar Wilde's 'A Good Woman': A Bibliographical Investigation into Magdalen MS. 300

by Sophie Duncan

Bodleian Library Record Vol 23 No 2 (October 2010), pp. 230-247.

Can science tell us what's objectively true?

by Brian Earp

Earp, B. D. (2011). Can science tell us what’s objectively true? The New Collection, Vol. 6., No. 1, 1-9. Featured article in the graduate journal of New College, Oxford.

Can science tell us what’s objectively true? Or is it merely a clever way to cure doubt – to give us something to... more Can science tell us what’s objectively true? Or is it merely a clever way to cure doubt – to give us something to believe in, whether it’s true or not? In this essay, I look at the pragmatist account of science expounded by Charles Sanders Peirce in his 1877 essay, ‘The Fixation of Belief’. Against Peirce, I argue that science does not come naturally to our species, nor does the doubting open-mindedness upon which its practice relies. To the extent that science is successful in ‘curing’ doubt, it’s because it tracks the real state of the world; and I argue that Peirce himself – his pragmatist narrative notwithstanding – is implicitly committed to this view as well.

Credal semantics of Bayesian transformations in terms of probability intervals

by Fabio Cuzzolin

Two new Bayesian approximations of belief functions based on convex geometry

by Fabio Cuzzolin

Credal semantics of Bayesian approximations in terms of probability intervals

by Fabio Cuzzolin