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Towards Unifying Perceptual Reasoning and Logical Reasoning

Hiroyuki Kido

TL;DR

The paper addresses the gap between perceptual inference and symbolic reasoning by proposing a unified Bayesian framework. The core construct is Generative Logic Models that jointly model data generation, model assignment, and truth interpretation of formulae, enabling inference from both data and stored knowledge without relying on ad hoc separation. Under the limit $\mu\to1$ and the model assumption $0\notin p(M)$, probabilistic conditioning $p(\alpha|\Delta)$ recovers logical consequence relations derived from maximal subsets (MCS) or maximal possible subsets (MPS). The work demonstrates two motivating examples for perception and logic, shows compatibility with maximum-likelihood estimates, and outlines future directions including dynamic perception and neuroscientific validation.

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.

Towards Unifying Perceptual Reasoning and Logical Reasoning

TL;DR

The paper addresses the gap between perceptual inference and symbolic reasoning by proposing a unified Bayesian framework. The core construct is Generative Logic Models that jointly model data generation, model assignment, and truth interpretation of formulae, enabling inference from both data and stored knowledge without relying on ad hoc separation. Under the limit and the model assumption , probabilistic conditioning recovers logical consequence relations derived from maximal subsets (MCS) or maximal possible subsets (MPS). The work demonstrates two motivating examples for perception and logic, shows compatibility with maximum-likelihood estimates, and outlines future directions including dynamic perception and neuroscientific validation.

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.
Paper Structure (3 sections, 1 theorem, 12 equations, 3 figures)

This paper contains 3 sections, 1 theorem, 12 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Motivating Examples
  3. Generative Logic Models

Key Result

proposition thmcounterproposition

The generative logical model satisfies the Kolmogorov's axioms.

Figures (3)

  • Figure 1: Most people tend to perceive a concave surface when a shadow appears in the upper portion of the disk. This is explained as the result of our unconscious belief that light sources typically come from above.
  • Figure 2: Data (left) and graphical model (right) for perceptual reasoning.
  • Figure 3: Data (left) and graphical model (right) for logical reasoning.

Theorems & Definitions (2)

  • proposition thmcounterproposition
  • proof