Rule of Assumption

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Sequent

The rule of assumption is a valid deduction sequent in propositional logic.


Proof Rule

An assumption may be introduced at any stage of an argument.


Sequent Form

For structure-technical reasons, the rule of assumption is symbolised by the sequent:

$p \vdash p$

In this form it is usually referred to as the Law of Identity.


Boolean Interpretation

The truth value of a propositional formula $\mathbf A$ under a boolean interpretation $v$ is given by:

$v \left({\mathbf A}\right) = \begin{cases} T & : v \left({\mathbf A}\right) = T \\ F & : v \left({\mathbf A}\right) = F \end{cases}$


Explanation

It does not matter whether the assumption is true -- all we are concerned about is making sure that any conclusion based on the assumptions made is as the result of a valid argument.

The introduction of an assumption $\phi$ into an argument by means of the Rule of Assumption can be interpreted in natural language as:

"Suppose it were true that $\phi$"

or:

"What if $\phi$ were true?"


Also known as

Some sources refer to the Rule of Assumption as the rule of assertion.


Also see