Some Properties of Plausible Reasoning

TL;DR

This paper explores a belief calculus framework for plausible reasoning, addressing issues like dualities in reasoning styles and their approximate nature, using Bayesian probability to unify defaults, likelihood, necessity, and possibility.

Contribution

It introduces a belief calculus system based on Bayesian probability to unify various plausible reasoning forms and discusses their properties and limitations.

Findings

Plausible reasoning forms can be grounded in Bayesian probability.

The system handles defaults, likelihood, necessity, and possibility.

Approximate reasoning and consistency are analyzed.

Abstract

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature of plausible reasoning. These issues have a common underlying theme: there should be an underlying belief calculus of which the many different reasoning forms are special cases, sometimes approximate. The system presented allows reasoning about defaults, likelihood, necessity and possibility in a manner similar to the earlier work of Adams. The system is based on the belief calculus of subjective Bayesian probability which itself is based on a few simple assumptions about how belief should be manipulated. Approximations, semantics, consistency and consequence results are presented for the system. While this puts these often discussed plausible reasoning forms on a probabilistic footing, useful application to practical problems remains an issue.