Rule of Assumption

Proof Rule
The rule of assumption is a valid deduction sequent in propositional logic: 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:

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

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

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: $\mathrm A$ or $\mathrm P$
 * 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?"

Also known as
Some sources refer to this as the rule of assertion.

Also see

 * Premise
 * Law of Identity

Technical Note
When invoking the Rule of Assumption in a tableau proof, use:



or:

where:
 * is the number of the line on the tableau proof where the assumption is to be invoked
 * is the statement of logic that is to be displayed in the Formula column, without the  delimiters
 * is the (optional) comment that is to be displayed in the Notes column.