David Billington

David Billington

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.

David Billington

Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles that clarifies what it means for a formal logic to do plausible reasoning is presented. A new propositional logic, called Propositional Plausible Logic (PPL), is defined and applied to some important examples. PPL is the only non-numeric non-monotonic logic we know of that satisfies all the principles and correctly reasons with all the examples. Some important results about PPL are proved.