Logic

Logic is the art and science behind reasoning which seeks to identify and understand the principles of valid inference and argument.

There are important properties that logical systems can have:

Consistency: which means that no theorem of the system contradicts another.
 
Soundness: which means that the system's rules of proof will never allow a false inference from a true premise. If a system is sound and its axioms are true then its theorems are also guaranteed to be true.

Completeness: which means that there are no true sentences in the system that cannot, at least in principle, be proved in the system.

Deductive reasoning is what must follow from given premises. An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion is false.

Inductive reasoning is the process of deriving a reliable generalization from observations. The task of providing this definition may be approached in various ways, some less formal than others. For the most part discussions of logic deal only with deductive logic.

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