Accept & Reject Statement-Based Uncertainty Models

We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss---as a bridge to existing frameworks---a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.Comment: 35 pages, 17 figure

Modelling practical certainty and its link with classical propositional logic

We model practical certainty in the language of accept & reject statement-based uncertainty models. We present three different ways, each time using a different nature of assessment: we study coherent models following from (i) favourability assessments, (ii) acceptability assessments, and (iii) indifference assessments. We argue that a statement of favourability, when used with an appropriate background model, essentially boils down to stating a belief of practical certainty using acceptability assessments. We show that the corresponding models do not form an intersection structure, in contradistinction with the coherent models following from an indifferenc assessment. We construct embeddings of classical propositional logic into each of our models for practical certainty

XSRL: An XML web-services request language

One of the most serious challenges that web-service enabled e-marketplaces face is the lack of formal support for expressing service requests against UDDI-resident web-services in order to solve a complex business problem. In this paper we present a web-service request language (XSRL) developed on the basis of AI planning and the XML database query language XQuery. This framework is designed to handle and execute XSRL requests and is capable of performing planning actions under uncertainty on the basis of refinement and revision as new service-related information is accumulated (via interaction with the user or UDDI) and as execution circumstances necessitate change

Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic

The CONEstrip algorithm

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs

A response to “Likelihood ratio as weight of evidence: a closer look” by Lund and Iyer

Recently, Lund and Iyer (L&I) raised an argument regarding the use of likelihood ratios in court. In our view, their argument is based on a lack of understanding of the paradigm. L&I argue that the decision maker should not accept the expert’s likelihood ratio without further consideration. This is agreed by all parties. In normal practice, there is often considerable and proper exploration in court of the basis for any probabilistic statement. We conclude that L&I argue against a practice that does not exist and which no one advocates. Further we conclude that the most informative summary of evidential weight is the likelihood ratio. We state that this is the summary that should be presented to a court in every scientific assessment of evidential weight with supporting information about how it was constructed and on what it was based