Symbols:Symbolic Logic/Deprecated Symbols

Deprecated Symbols of Symbolic Logic

This page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.

Texts on logic often tend to use these symbols in preference to those used in mathematics.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ the intention is to present a consistent style, and so these symbols are to be considered deprecated.

Therefore

$\therefore$

Therefore

If statement $p$ logically implies statement $q$, then we may say:

$p$, therefore $q$

and denote it:

$p \therefore q$

An alternative to $p \vdash q$, the preferred notation on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(p \therefore q\) is p \therefore q .

And

$\cdot$

And

A binary operation on two propositions.

$P \cdot Q$ means $P$ is true and $Q$ is true.

In this usage, it is called dot.

An alternative to $P \land Q$, usually used by logicians.

The $\LaTeX$ code for \(P \cdot Q\) is P \cdot Q .

Ampersand

$\&$

$P \mathop \& Q$ means $P$ is true and $Q$ is true.

An alternative to $P \land Q$, which is what is usually used by logicians.

The $\LaTeX$ code for \(P \mathop \& Q\) is P \mathop \& Q  or P \mathop \And Q.

Disjunction

$+$

Or.

A binary operation on two propositions.

$P + Q$ means either $P$ is true or $Q$ is true or both.

An alternative to $P \lor Q$, which is what is usually used by logicians.

The $\LaTeX$ code for \(P + Q\) is P + Q .

Minus

$-$

Not.

A unary operation on a proposition.

$-Q$ means $Q$ is not true.

An alternative to $\neg$, which is what is usually used by logicians.

The $\LaTeX$ code for \(-Q\) is -Q .

Arrow

$\to$

Implies:

An alternative to $P \implies Q$.

The $\LaTeX$ code for \(P \to Q\) is P \to Q .

Hook

$\supset$

Implies.

An alternative to $P \implies Q$.

The $\LaTeX$ code for \(P \supset Q\) is P \supset Q .

Double Arrow

$\leftrightarrow$

Biconditional.

An alternative to $P \iff Q$.

The $\LaTeX$ code for \(P \leftrightarrow Q\) is P \leftrightarrow Q .

Identity

$\equiv$

Biconditional.

An alternative to $P \equiv Q$.

The $\LaTeX$ code for \(P \equiv Q\) is P \equiv Q .

Tilde

$\sim$

Not.

A unary operation on a proposition.

$\sim Q$ means $Q$ is not true.

An alternative to $\neg$, which is what is usually used by logicians.

The $\LaTeX$ code for \(\sim Q\) is \sim Q .

Sheffer Stroke

$\mid$

Logical NAND.

A binary operation on two propositions.

$P \mid Q$ means not both $P$ and $Q$ together

This is known as the Sheffer stroke.

The $\LaTeX$ code for \(P \mid Q\) is P \mid Q .

Modified Ampheck

$P \mathop {\bar \curlywedge} Q$

Logical NAND.

A binary operation on two propositions.

$P \mathop {\bar \curlywedge} Q$ means not both $P$ and $Q$ together.

The $\LaTeX$ code for \(P \mathop {\bar \curlywedge} Q\) is P \mathop {\bar \curlywedge} Q .

Ampheck

$\curlywedge$

Logical NOR.

A binary operation on two propositions.

$P \curlywedge Q$ means neither $P$ nor $Q$.

The $\LaTeX$ code for \(P \curlywedge Q\) is P \curlywedge Q .