# nLab propositional logic

foundations

## Foundational axioms

foundational axiom

# Contents

## 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 $P\left(x\right)$ in a $0$th-order proposition might as well be thought of as atomic.

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.

Revised on November 6, 2012 17:54:16 by Urs Schreiber (131.174.40.32)