Modelling reasoning processes in natural agents: a partial-worlds-based logical framework for elemental non-monotonic inferences and learning
Résumé
In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inferences for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor's cumulative models. We show that the inference relations they induce form a strict subclass of cumulative relations, and tackle the issue of providing sound and complete sets of rules to characterize them. Taking inspiration from Gabbay & Schlechta's work on preferential structures (Gabbay & Schlechta, 2008, 2009), we analyse the question in terms of definable sets of partial worlds, and conclude that completeness is probably unreachable using a standard propositional language. This brings us to enrich our language with an additional connective ‖, allowing to distinguish between two kinds of disjunctions in partial worlds context. Within this renewed framework, we provide two representation theorems: one for inference relations induced by precisification-free smooth models, and the other for inference relations induced by precisification-free ranked models. Finally we give an aperçu of how partial worlds models lend themselves to the modelling of learning.
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