Richard Booth 0001

NMR Workshop 2024 Invited Paper

Interval Orders and Biorders: Under-explored Playgrounds for NMR and Belief Revision (Invited Talk, Abstract)

• Richard Booth 0001

The notion of orderings over possible worlds to represent comparative normality or plausibility is a fundamental tool in the study of semantics for nonmonotonic reasoning (NMR) and belief revision (BR). The dominant model is that of a total preorder, which is central to AGM belief revision and to rational consequence in KLM-style preferential reasoning. Other, more general, types of orderings, specifically interval orders and biorders, have been studied in the theory of rational choice, but have received less attention in NMR and BR. Interval orders, introduced by Fishburn, associate to each possible world a non-negative interval of plausibility, while biorders, studied by Aleskerov, Bouyssou and Monjardet, generalise interval orders by allowing the intervals to be have negative length. This talk, based on recent and ongoing collaboration with Ivan Varzinczak, will focus on these lesser-known kinds of ordering. Specifically we will look at how interval orders can be used to address the problem of conditional inference, and how biorders offer a fresh perspective on credibility-limited belief revision.

NMR Workshop 2024 Conference Paper

The Role of Syntax in Inductive Inference: A Property-based Study

• Jesse Heyninck
• Richard Booth 0001
• Thomas Andreas Meyer

The study of inference operators frequently involves the introduction of properties to which such operators should conform. Amongst other advantages, the property-based approach helps to restrict the range of operators, and to classify and categorise the type of inference being studied. This paper continues this tradition by proposing a number of properties for the class of inductive inference operators. We study the interaction of these properties, both with one another, and with other well-known properties for inductive inference. We also test a number of well-known inductive inference operators against the newly proposed, and some existing properties.

NMR Workshop 2022 Conference Paper

Truth-Tracking with Non-Expert Information Sources

• Joseph Singleton
• Richard Booth 0001

We study what can be learned when receiving reports from multiple non-expert information sources. We suppose that sources report all that they consider possible, given their expertise. This may result in false and inconsistent reports when sources lack expertise on a topic. A learning method is truth-tracking, roughly speaking, if it eventually converges to correct beliefs about the “actual” world. This involves finding both the actual state of affairs in the domain described by the sources, and finding the extent of the expertise of the sources themselves. We investigate the extent to which truth-tracking is possible, and describe what information can be learned even if the actual world cannot be pinned down uniquely. We find that a broad spread of expertise among the sources allows the actual state of affairs to be found, even if no individual source is an expert on all topics. On the other hand, narrower expertise at the individual level allows the actual expertise to be found more easily. Finally, we turn to learning methods themselves: we provide a postulate-based characterisation of truth-tracking for general methods under mild assumptions, before looking at a specific class of methods well-known from the belief change literature.

LORI Conference 2019 Conference Paper

Elementary Iterated Revision and the Levi Identity

• Jake Chandler
• Richard Booth 0001

Abstract Recent work has considered the problem of extending to the case of iterated belief change the so-called ‘Harper Identity’ (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators–natural, restrained and lexicographic, for which we provide here the first collective characterisation in the literature, under the appellation of ‘elementary’ operators. We consider two prima facie plausible ways of extending (LI). The first proposal involves the use of the rational closure operator to offer a ‘reductive’ account of iterated revision in terms of iterated contraction. The second, which doesn’t commit to reductionism, was put forward some years ago by Nayak et al. . We establish that, for elementary revision operators and under mild assumptions regarding contraction, Nayak’s proposal is equivalent to a new set of postulates formalising the claim that contraction by \(\lnot A\) should be considered to be a kind of ‘mild’ revision by A. We then show that these, in turn, under slightly weaker assumptions, jointly amount to the conjunction of a pair of constraints on the extension of (HI) that were recently proposed in the literature. Finally, we consider the consequences of endorsing both suggestions and show that this would yield an identification of rational revision with natural revision. We close the paper by discussing the general prospects for defining iterated revision in terms of iterated contraction.

ECAI Conference 2014 Conference Paper

Abduction and Dialogical Proof in Argumentation and Logic Programming

• Richard Booth 0001
• Dov M. Gabbay
• Souhila Kaci
• Tjitze Rienstra
• Leendert W. N. van der Torre

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i. e. , finding hypotheses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.

ECAI Conference 2014 Conference Paper

Credibility-Limited Improvement Operators

• Richard Booth 0001
• Eduardo L. Fermé
• Sébastien Konieczny
• Ramón Pino Pérez

In this paper we introduce and study credibility-limited improvement operators. The idea is to accept the new piece of information if this information is judged credible by the agent, so in this case a revision is performed. When the new piece of information is not credible then it is not accepted (no revision is performed), but its plausibility is still improved in the epistemic state of the agent, similarly to what is done by improvement operators. We use a generalized definition of Darwiche and Pearl epistemic states, where to each epistemic state can be associated, in addition to the set of accepted formulas (beliefs), a set of credible formulas. We provide a syntactic and semantic characterization of these operators.

JELIA Conference 2012 Conference Paper

PTL: A Propositional Typicality Logic

• Richard Booth 0001
• Thomas Andreas Meyer
• Ivan Varzinczak

Abstract We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a formula holds. The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that rational consequence relations can be embedded in our logic. Moreover we show that we can define consequence relations on the language of PTL itself, thereby moving beyond the propositional setting. Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds for rational consequence and belief revision on PTL. We investigate entailment for PTL, and propose two appropriate notions thereof.

ECAI Conference 2010 Conference Paper

Horn Belief Change: A Contraction Core

• Richard Booth 0001
• Thomas Andreas Meyer
• Ivan Varzinczak
• Renata Wassermann

We show that Booth et al. 's Horn contraction based on infra-remainder sets corresponds exactly to kernel contraction for belief sets. This result is obtained via a detour through Horn contraction for belief bases, which supports the conjecture that Horn belief change is best viewed as a "hybrid" version of belief set change and belief base change. Moreover, the link with base contraction gives us a more elegant representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

ECAI Conference 2010 Conference Paper

Learning conditionally lexicographic preference relations

• Richard Booth 0001
• Yann Chevaleyre
• Jérôme Lang
• Jérôme Mengin
• Chattrakul Sombattheera

We consider the problem of learning a user's ordinal preferences on a multiattribute domain, assuming that her preferences are lexicographic. We introduce a general graphical representation called LP-trees which captures various natural classes of such preference relations, depending on whether the importance order between attributes and/or the local preferences on the domain of each attribute is conditional on the values of other attributes. For each class we determine the Vapnik-Chernovenkis dimension, the communication complexity of preference elicitation, and the complexity of identifying a model in the class consistent with a set of user-provided examples.

LORI Conference 2009 Conference Paper

A General Family of Preferential Belief Removal Operators

• Richard Booth 0001
• Thomas Andreas Meyer
• Chattrakul Sombattheera

Abstract Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in [5]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of [5] to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases.

ECAI Conference 2004 Conference Paper

A Unifying Semantics for Belief Change

• Richard Booth 0001
• Samir Chopra
• Thomas Andreas Meyer
• Aditya Ghose

NMR Workshop 2004 Conference Paper

A unifying semantics for belief change

• Richard Booth 0001
• Samir Chopra
• Thomas Andreas Meyer
• Aditya Ghose

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 ordering, we look at using an extra ordering to aid in guiding the process of belief change. We show that this 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 (Alchourrón, Gärdenfors, & Makinson 1985), severe withdrawal (Rott & Pagnucco 1999), systematic withdrawal (Meyer et al. 2002), and the linear liberation and σ-liberation operators of (Booth et al. 2003). Our approach also identifies novel classes of belief change operators that are worth further investigation.

TARK Conference 2003 Conference Paper

Belief liberation (and retraction)

• Richard Booth 0001
• Samir Chopra
• Aditya Ghose
• Thomas Andreas Meyer

We provide a formal study of belief retraction operators that do not necessarily satisfy the (Inclusion) postulate. Our intuition is that a rational description of belief change must do justice to cases in which dropping a belief can lead to the inclusion, or 'liberation', of others in an agent's corpus. We provide a few possible weakenings of the (Inclusion) postulate and then provide two models of liberation via retraction operators, a-liberation and linear liberation. We show that the class of c-liberation operators is included in the class of linear ones and provide axiomatic characterisations for each class. We also show how any given retraction operator (including the liberation operators) can be 'converted' into either a withdrawal operator (i. e. , -satisfying (Inclusion)) or a revision operator via (a slight v~iant of) the Harper Identity and the Levi Identity respectively.

UAI Conference 2003 Conference Paper

On revising fuzzy belief bases

• Richard Booth 0001
• Eva Richter