+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Foundations +-- {: .hide} [[!include foundations - contents]] =-- =-- =-- # Contents * table of contents {: toc} ## Idea __Propositional logic__, also called __$0$th-order logic__ and __sentential logic__, is that part of [[logic]] that deals only with [[propositions]] with no [[bound variables]]. Compare [[predicate logic]], or $1$st-order logic, and [[higher-order logic]]. Note that while one can have *free* variables in $0$th-order logic, one cannot really do anything with them; each $P(x)$ in a $0$th-order proposition might as well be thought of as atomic. This can be understood more cleanly in the language of many-sorted logic, where each variable has to have a specified sort. Then ordinary predicate logic has exactly one sort, usually unnamed. Propositional logic is for a signature with no sorts, hence no variables at all. A __propositional calculus__, also called __sentential calculus__, is simply a system for describing and working with propositional logic. The precise form of such a calculus (and hence of the logic itself) depends on whether one is using [[classical logic]], [[intuitionistic logic]], [[linear logic]], etc; see those articles for details. ## Related concepts * [[logic]] * **propositional logic** (0th order) * [[predicate logic]] (1st order) * [[higher order logic]] * [[modal logic]] * [[propositional logic as a dependent type theory]] * [[zeroth-order set theory]] [[!redirects propositional logic]] [[!redirects propositional calculus]] [[!redirects 0th-order logic]] [[!redirects 0-th-order logic]] [[!redirects zeroth-order logic]] [[!redirects zeroeth-order logic]] [[!redirects 0th order logic]] [[!redirects 0-th order logic]] [[!redirects zeroth order logic]] [[!redirects zeroeth order logic]] [[!redirects sentential logic]] [[!redirects sentential calculus]] [[!redirects sentensial logic]] [[!redirects sentensial calculus]] [[!redirects propositional logics]]