Plausible Reasoning and First-Order Plausible Logic
Summary: arXiv:2604.19036v1 Announce Type: new
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.
Introduction to Plausible Logic
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.
Overview of Principles
The principles of plausible reasoning can be categorized into two groups:
- Necessary Principles: These are fundamental to the framework of plausible reasoning and must be adhered to in every logical analysis.
- Desirable Principles: While beneficial, these principles are not essential and can be relaxed in certain scenarios.
Necessary Principles
There are 14 necessary principles that govern the function of plausible reasoning:
- Principle 1: Consistency in reasoning.
- Principle 2: Relevance of facts.
- Principle 3: The role of defeasible statements.
- Principle 4: Inference based on evidence.
- Principle 5: The transitive property of conclusions.
- Principle 6: Clarity in definitions.
- Principle 7: Contextual consideration.
- Principle 8: Avoidance of contradictions.
- Principle 9: The principle of charity in interpretations.
- Principle 10: The balance of certainty and uncertainty.
- Principle 11: The role of temporal factors.
- Principle 12: The significance of counterexamples.
- Principle 13: The importance of coherence.
- Principle 14: Adaptability of conclusions.
Desirable Principles
There are 3 desirable principles that enhance the robustness of plausible reasoning:
- Principle 1: Flexibility in reasoning approaches.
- Principle 2: Integration of interdisciplinary insights.
- Principle 3: (Not formally stated).
Conclusion
This article serves as a preliminary exploration into the field of plausible reasoning and first-order plausible logic. The proofs of all the results are in PRPL, so they are omitted in this article. Future discussions will expand on these principles and their applications in various domains of knowledge.