Definition:Language of Propositional Logic/Labeled Tree

Definition
There are many formal languages expressing propositional logic.

The formal language used on is defined on Definition:Language of Propositional Logic.

This page defines the formal language $\LL_0$ used in:



Explanations are omitted as this is intended for reference use only.

Letters
The letters used are an infinite set of symbols $\PP_0$.

This is the same as the definition.

Connectives
The following connectives are used:

See the definition.

Collation System
The collation system used is that of labeled trees and adding ancestors.

See the definition.

Formal Grammar
The following bottom-up formal grammar is used.

Let $\PP_0$ be the vocabulary of $\LL_0$.

The WFFs of $\LL_0$ are the smallest set $\FF$ of labeled trees such that:

Graphically, this means one has the following means to construct WFFs:


 * $\begin{xy}\xymatrix{

p & & \neg \ar@{-}[d] & & & \mathsf B \ar@{-}[ld] \ar@{-}[rd]

\\ & & <{\sf WFF}> & & <{\sf WFF}> & & <{\sf WFF}> }\end{xy}$ See the definition.

Also see

 * Definition:Language of Propositional Logic