Rule of Assumption
Sequent
The rule of assumption is a valid argument in many proof systems, including natural deduction.
Proof Rule
- An assumption $\phi$ 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:
- $\map v {\mathbf A} = \begin{cases}
\T & : \map v {\mathbf A} = \T \\ \F & : \map v {\mathbf A} = \F \end{cases}$
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.