Towards Unifying Perceptual Reasoning and Logical Reasoning

TL;DR

This paper proposes a unified probabilistic model that integrates perceptual and logical reasoning as Bayesian inference, providing a common framework for deriving knowledge from data and other knowledge.

Contribution

It introduces a simple probabilistic model that unifies perceptual and logical reasoning processes within a Bayesian inference framework.

Findings

The model successfully unifies perceptual and logical reasoning.

It characterizes logical consequence relations within the probabilistic framework.

The approach supports deriving knowledge from data and existing knowledge.

Abstract

An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as Bayesian inference. In this paper, we give a simple probabilistic model that is applicable to both perceptual reasoning and logical reasoning. We show that the model unifies the two essential processes common in perceptual and logical systems: on the one hand, the process by which perceptual and logical knowledge is derived from another knowledge, and on the other hand, the process by which such knowledge is derived from data. We fully characterise the model in terms of logical consequence relations.