Rule of Assumption/Proof Rule

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Proof Rule

The rule of assumption is a valid argument in many proof systems, including natural deduction.

As a proof rule it is expressed in the form:


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


Tableau Form

Let $\phi$ be a propositional formula.

The Rule of Assumption is invoked for $\phi$ in a tableau proof in the following manner:

Pool:    The line on which the Rule of Assumption is invoked      
Formula:    $\phi$      
Description:    Assumption or Premise      
Depends on:    (None)      
Abbreviation:    $\mathrm A$ or $\mathrm P$ accordingly      


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


Technical Note

When invoking the Rule of Assumption in a tableau proof, use the {{Assumption}} template:

{{Assumption|line|statement}}

or:

{{Assumption|line|statement|comment}}

where:

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


When the assumption being made is a premise, use the {{Premise}} template:

{{Premise|line|statement}}

or:

{{Premise|line|statement|comment}}

in the same manner as above.


Sources

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