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The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of [[semantics]]. Inductive validity, on the other hand, requires us to define a reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use logical association [[rule induction]], while others may use [[mathematical model]]s of probability such as [[decision tree]]s. For the most part this discussion of logic deals only with deductive logic.
Abductive reasoning is a form of [[inference]] which goes from an observation to a [[theory]] which accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. One can understand abductive reasoning as "inference to the best explanation".<ref>Sober, Elliot. Core Questions in Philosophy,5th edition.</ref>
==Critical thinking==
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