Rule of Assumption

Context
The rule of assumption is one of the axioms of natural deduction.

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

Sequent Form
For structure-technical reasons, an assumption $p$ is symbolised by the sequent:


 * $p \vdash p$

which expresses that: "Assuming $p$ is true, $p$ is true."

Tableau Form
In a tableau proof, the Rule of Assumption can be invoked in the following manner:


 * Pool: Empty
 * Formula: The desired assumption $p$
 * Abbreviation: $\textrm {A}$ or $\textrm P$
 * Depends on: Nothing

To improve the readability of tableau proofs, the letter $\mathrm P$ is used for premises, and the letter $\mathrm A$ for assumptions that will be discharged later in the proof.

Explanation
There is no question of making sure that the assumption is true - all we are concerned about is making sure that any conclusion based on the assumptions made is valid.

The introduction of an assumption $p$ into an argument by means of the Rule of Assumption can be interpreted in natural language as: "What if $p$ were true?"