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.
Propositional calculus. S.Yu. Maslov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Propositional_calculus&oldid=12192