# Logical reasoning

Two kinds of **logical reasoning** are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or *premise*, a conclusion or *logical consequence* and a rule or *material conditional* that implies the *conclusion* given the *precondition*, one can explain the following.

- Deductive reasoning determines whether the truth of a
*conclusion*can be determined for that*rule*, based solely on the truth of the premises. Example: "When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet." Mathematical logic and philosophical logic are commonly associated with this type of reasoning. - Inductive reasoning attempts to support a determination of the
*rule*. It hypothesizes a*rule*after numerous examples are taken to be a*conclusion*that follows from a*precondition*in terms of such a*rule*. Example: "The grass got wet numerous times when it rained, therefore: the grass always gets wet when it rains." This type of reasoning is commonly associated with generalization from empirical evidence. While they may be persuasive, these arguments are not deductively valid: see the problem of induction. - Abductive reasoning, sometimes called
*inference to the best explanation*, selects a cogent set of*preconditions*. Given a true*conclusion*and a*rule*, it attempts to select some possible*premises*that, if true also, can support the*conclusion*, though not uniquely. Example: "When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained." This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Diagnosticians, detectives, and scientists often use this type of reasoning.

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Within the context of a mathematical model, these three kinds of reasoning can be described as follows. The construction/creation of the structure of the model is *abduction*. Assigning values (or probability distributions) to the parameters of the model is *induction*. Executing/running the model is *deduction*.

Other kinds of reasoning beside the three common categories above are:

See Non-demonstrative reasoning for a comparison of these other kinds of reasoning.