Propositions can be formulated in natural languages, e.g. the English sentence "It is raining" is a proposition. However, natural languages have complex grammars and are too ambiguous to strictly define a logical calculus of a propositional logic. Therefore, we will concentrate on the main elements needed to construct a propositional logic and leave everything else as a superfluous ballast out of our definition.

Definition: Signature of Propositional Logic - PL0

The signature $(V,F,P)$ of a propositional logic consists of

Because the set of predicates $P$ is empty, the propositional logic is also called zeroth-order predicate logic and denoted by $PL0$.

Definitions: 1
Parts: 2

Thank you to the contributors under CC BY-SA 4.0!




  1. Beierle, C.; Kern-Isberner, G.: "Methoden wissensbasierter Systeme", Vieweg, 2000