# Propositional calculus

A general name for a deductive system whose deducible objects can be interpreted as statements formed from simple (i.e. not analyzable in the framework of propositional calculus) statements using propositional connectives (such as "not" , "and" , "or" , "if …, then …" , etc.; see Logical calculus). The most important example is the classical propositional calculus, in which statements may assume two values — "true" or "false" — and the deducible objects are precisely all identically true statements. The interest in propositional calculi is due to the fact that they form the base of almost all logical-mathematical theories, and usually combine relative simplicity with a rich content. In particular, many theoretical and applied problems can be reduced to some problem in the classical propositional calculus.

For references see Logical calculus.

**How to Cite This Entry:**

Propositional calculus. S.Yu. Maslov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Propositional_calculus&oldid=12192