<p>Factual reasoning is reasoning with statements that are certain, called facts. Classical&nbsp;propositional logic is often used for such reasoning. However classical propositional logic has two faults. Its most serious fault is the irrational way it behaves when&nbsp;the statements are inconsistent. The second, less serious, fault is that there is an intuitive&nbsp;understanding of the meaning of &lsquo;follows from&rsquo; that classical propositional logic&nbsp;does not capture. Various new consistent subsets of a set of inconsistent statements are&nbsp;investigated. This yields new more rational propositional logics for factual reasoning&nbsp;that capture the missing intuitive meaning of &lsquo;follows from&rsquo;.</p><p>Logics that do factual reasoning have properties that can be expressed by using&nbsp;consequence functions. A consequence function is meant to be a function whose input&nbsp;is a set of formulas and whose output is the set of consequences of those formulas.&nbsp;However, there is no adequate definition of what a consequence function is. A new&nbsp;definition of what a consequence function should be is proposed and shown to have&nbsp;many desirable properties.</p><p>Plausible reasoning is reasoning with statements that are either facts, or are likely,&nbsp;called defeasible statements. Moreover all defeasible statements have the same likelihood;&nbsp;hence there are no numbers, like probabilities, involved. Many principles of&nbsp;plausible reasoning are suggested and several important plausible reasoning examples&nbsp;are considered. A propositional logic is defined that satisfies all the principles and&nbsp;reasons correctly with all the examples. As far as we are aware, this is the only such&nbsp;logic.</p>