nLab propositional logic





The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms



Propositional logic, also called 00th-order logic and sentential logic, is that part of logic that deals only with propositions with no bound variables.

Compare predicate logic, or 11st-order logic, and higher-order logic. Note that while one can have free variables in 00th-order logic, one cannot really do anything with them; each P(x)P(x) in a 00th-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.

Last revised on October 14, 2022 at 17:36:09. See the history of this page for a list of all contributions to it.