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Logic (from the Ancient Greek: λογική, translit. logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. (In ordinary discourse, inferences may be signified by words such as therefore, hence, ergo, and so on.)

There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference, including fallacies, and the study of semantics, including paradoxes. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century), and recently logic has been studied in computer science, linguistics, psychology, and other fields.

In the formal languages used in mathematical logic and computer science, a well-formed formula or simply formula[2] (often abbreviated wff, pronounced "wiff" or "wuff") is an idea, abstraction or concept which is expressed using the symbols and formation rules (also called the formal grammar) of a particular formal language. To say that a string of symbols is a wff with respect to a given formal grammar is equivalent to saying that belongs to the language generated by . A formal language can be identified with the set of its wffs.
Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform.

A prolific writer, he was also a populariser of philosophy and a commentator on a large variety of topics, ranging from very serious issues to those much less so. Continuing a family tradition in political affairs, he was a prominent anti-war activist, championing free trade between nations and anti-imperialism.

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  1. Godel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter
  2. Because non-well-formed formulas are rarely considered, some authors ignore them altogether. For these authors, "formula" and "well-formed formula" are synonyms. Other authors use the term "formula" for any string of symbols in the language; certain of these strings are then singled out as the well-formed formulas.

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