Arthur Van Camp, Gert de Cooman

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Modelling practical certainty and its link with classical propositional logic

Abstract

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 not an intersection structure, in contradistinction with the coherent models following from an indifference assessment. We construct embeddings of classical propositional logic into each of our models for practical certainty.

Keywords

Imprecise probabilities, accept and reject statement-based uncertainty models, classical propositional logic, belief structure

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E-mail addresses

Arthur Van Camp		arthur.vancamp@ugent.be
Gert de Cooman		gert.decooman@ugent.be