Definition:Entailment

Definition

entailment is the logical connective defined for statements $p$ and $q$ as follows:

Let $p$ be relevant to, and actually used in, the statement that is $q$.

Let $q$ be true if $p$ true.

Then $p$ entails $q$:

$p \boldsymbol \prec q$

To denote that $p$ entails $q$, $\mathsf{Pr} \infty \mathsf{fWiki}$ uses the notation $p \boldsymbol \prec q$.

Sources which use the symbol $\to$ for conventional implication may then use $\implies$ for entailment.

The $\LaTeX$ code for $p \boldsymbol \prec q$ is p \boldsymbol \prec q .

It does this by insisting that, before $p$ can imply $q$, it must be relevant to and actually used in the definition of $q$.

$\neg p, p \lor q \vdash p \implies q$

is rejected.