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Researcher profile

Richard Booth

Richard Booth contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial Intelligenceastro-ph.EPastro-ph.GALogic in Computer ScienceMultiagent Systems

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Published work

5 published item(s)

preprint2026arXiv

Interval Orders, Biorders and Credibility-limited Belief Revision

Rational belief revision is commonly viewed as being based on a preference order between possible worlds, with the resulting new belief set being those sentences true in all the most preferred models of the incoming new information. Usually, such a preference order is taken to be a total preorder. Nevertheless, there are other, more general classes of ordering that can also be employed. In this paper, we explore two such classes that have been studied within the theory of rational choice but have seen limited or no application in belief revision. We begin with interval orders, introduced by Fishburn in the '80s, which associate with each possible world a nonnegative `interval' of plausibility. We then move on to biorders, studied by Aleskerov, Bouyssou, and Monjardet, which generalise interval orders by allowing the intervals to have negative lengths, a feature that can be used to capture a notion of dissonance or instability. We provide axiomatic characterisations of these two resulting families of belief revision operators, as well as of two further families of interest that lie between interval orders and biorders. We show that while biorder-based revisions satisfy the Success postulate, they do not always yield consistent outputs. By modifying their definition to discard inputs that lead to inconsistency as `incredible', we derive new families of so-called non-prioritised revision that satisfy the Consistency postulate, but not the Success one. These families are linked to credibility-limited revision operators of Hansson et al., but for which the set of credible sentences does not satisfy the single-sentence closure condition. We argue that the biorder-based approach is well-suited for scenarios where an agent might initially reject new information, but may accept it when presented with additional explanation.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Rankings for Bipartite Tournaments via Chain Editing

Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity compete indirectly via matches against players of the opposite kind; examples include education (students/exam questions) and solo sports (golfers/courses). In particular, we look to find rankings via chain graphs, which correspond to bipartite tournaments in which the sets of adversaries defeated by the players on one side are nested with respect to set inclusion. Tournaments of this form have a natural and appealing ranking associated with them. We apply chain editing -- finding the minimum number of edge changes required to form a chain graph -- as a new mechanism for tournament ranking. The properties of these rankings are investigated in a probabilistic setting, where they arise as maximum likelihood estimators, and through the axiomatic method of social choice theory. Despite some nice properties, two problems remain: an important anonymity axiom is violated, and chain editing is NP-hard. We address both issues by relaxing the minimisation constraint in chain editing, and characterise the resulting ranking methods via a greedy approximation algorithm.

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preprint2020arXiv

On Rational Entailment for Propositional Typicality Logic

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.

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preprint2020arXiv

Revision by Conditionals: From Hook to Arrow

The belief revision literature has largely focussed on the issue of how to revise one's beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How might one extend a revision operator to handle conditionals as input? Our approach to this question of 'conditional revision' is distinctive insofar as it abstracts from the controversial details of how to revise by factual sentences. We introduce a 'plug and play' method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our approach is achieved by having the result of a conditional revision by a Ramsey Test conditional ('arrow') determined by that of a plain revision by its corresponding material conditional ('hook'). It is shown to satisfy a number of new constraints that are of independent interest.

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preprint2018arXiv

Gas density perturbations induced by forming planet(s) in the AS 209 protoplanetary disk as seen with ALMA

The formation of planets occurs within protoplanetary disks surrounding young stars, resulting in perturbation of the gas and dust surface densities. Here, we report the first evidence of spatially resolved gas surface density ($Σ_{g}$) perturbation towards the AS~209 protoplanetary disk from the optically thin C$^{18}$O ($J=2-1$) emission. The observations were carried out at 1.3~mm with ALMA at a spatial resolution of about 0.3$\arcsec$ $\times$ 0.2$\arcsec$ (corresponding to $\sim$ 38 $\times$ 25 au). The C$^{18}$O emission shows a compact ($\le$60~au), centrally peaked emission and an outer ring peaking at 140~au, consistent with that observed in the continuum emission and, its azimuthally averaged radial intensity profile presents a deficit that is spatially coincident with the previously reported dust map. This deficit can only be reproduced with our physico-thermochemical disk model by lowering $Σ_{gas}$ by nearly an order of magnitude in the dust gaps. Another salient result is that contrary to C$^{18}$O, the DCO$^{+}$ ($J=3-2$) emission peaks between the two dust gaps. We infer that the best scenario to explain our observations (C$^{18}$O deficit and DCO$^{+}$ enhancement) is a gas perturbation due to forming-planet(s), that is commensurate with previous continuum observations of the source along with hydrodynamical simulations. Our findings confirm that the previously observed dust gaps are very likely due to perturbation of the gas surface density that is induced by a planet of at least 0.2~M$\rm_{Jupiter}$ in formation. Finally, our observations also show the potential of using CO isotopologues to probe the presence of saturn mass planet(s).

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