Possibilistic reasoning from partially ordered belief bases with the sure thing principle

Abstract

We consider the problem of reasoning from logical bases equipped with a partial order expressing relative certainty, with a view to construct a partially ordered deduc-tive closure via syntactic inference. At the syntactic level we use a language expressing pairs of related formulas and axioms describing the properties of the order. Reasoning about uncertainty using possibility theory relies on the idea that if an agent believes each among two propositions to some extent, then this agent should believe their conjunction to the same extent. This principle is known as adjunction. Adjunction is often accepted in epistemic logic but fails with probabilistic reasoning. In the latter, another principle prevails, namely the sure thing principle, that claims that the certainty ordering between propositions should be invariant to the addition or deletion of possible worlds common to both sets of models of these propositions. Pursuing our work on relative certainty logic based on possibility theory, we propose a qualitative likelihood logic that respects the sure thing principle, albeit using a likelihood relation that preserves adjunction.