Plausible Reasoning and First-Order Plausible Logic

TL;DR

This paper introduces Plausible Logic, a first-order logic framework for plausible reasoning that operates without probabilities, satisfying most desirable principles and providing multiple reasoning algorithms.

Contribution

It defines a novel first-order plausible logic system with multiple algorithms, addressing key principles of plausible reasoning and demonstrating correctness on examples.

Findings

Plausible Logic satisfies 14 necessary and 3 desirable principles.

It includes 8 reasoning algorithms for different plausible reasoning scenarios.

The logic correctly reasons with all considered examples.

Abstract

Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers. So there are no probabilities or suchlike involved. Seventeen principles of logics that do plausible reasoning are suggested and several important plausible reasoning examples are considered. There are 14 necessary principles and 3 desirable principles, one of which is not formally stated. A first-order logic, called Plausible Logic (PL), is defined that satisfies all but two of the desirable principles and reasons correctly with all the examples. As far as we are aware, this is the only such logic. PL has 8 reasoning algorithms because, from a given plausible reasoning situation, there are different sensible conclusions. This article is a condensation of my book `Plausible Reasoning and Plausible Logic' (PRPL), which is to be submitted. Each section of this article corresponds to a chapter in PRPL, and vice versa. The proofs of all the results are in PRPL, so they are omitted in this article.