Plausible Reasoning and First-Order Plausible Logic

2026-04-22 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This article introduces Plausible Logic (PL), a first-order logic designed for plausible reasoning, which handles statements that are usually true but can be occasionally false without using numerical probabilities. PL is built upon 17 principles, including 14 necessary and 3 desirable ones, derived from analyzing various plausible reasoning examples like the 3-lottery and the Ambiguity Puzzle. The logic defines a "plausible-description" using axioms, rules (strict, defeasible, warning), and a priority relation. It features 8 distinct proof algorithms, such as factual ($varphi$), ambiguity-blocking ($eta$, $ heta$), and ambiguity-propagating ($pi$, $psi$) algorithms, which form a linear hierarchy of reliability. PL satisfies all but two desirable principles and correctly addresses the considered examples. Proofs in PL are represented as rooted acyclic digraphs (rads), and the logic incorporates a truth theory with at least three truth values: usually true (t), usually false (f), ambiguous (a), and undetermined (u).

Key takeaway

For AI Scientists and Research Scientists developing knowledge representation and reasoning systems, Plausible Logic provides a robust, non-probabilistic framework for handling uncertainty. Its distinct proof algorithms offer fine-grained control over how ambiguity is managed, allowing you to tailor reasoning to specific application contexts, such as civil law's "balance of probabilities" versus criminal law's "beyond reasonable doubt." Consider implementing PL's hierarchical algorithms to achieve varying confidence levels in your system's conclusions.

Key insights

Plausible Logic offers a non-numeric, first-order framework for reasoning with defeasible statements and managing ambiguity.

Principles

• Distinguish factual from plausible statements.
• Plausible reasoning is non-monotonic and non-conjunctive.
• Multiple proof algorithms handle different ambiguity levels.

Method

PL uses a proof function $P$ and 8 algorithms to evaluate evidence for/against a formula, considering rule priorities and preventing loops via histories. Proofs are structured as rooted acyclic digraphs.

In practice

• Use $\varphi$ for factual certainty.
• Select $\beta$ for ambiguity-blocking, 'best bet' reasoning.
• Choose $\pi$ for cautious, ambiguity-propagating conclusions.

Topics

• Plausible Reasoning
• First-Order Plausible Logic
• Defeasible Statements
• Non-Monotonic Logic
• Proof Algorithm Hierarchy

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.