Rule of Assumption/Proof Rule
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
- This is a rule of inference of the following proof system:
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 invokedstatement
is the statement of logic that is to be displayed in the Formula column, without the$ ... $
delimiterscomment
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
- 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 3$
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2.3$: Natural Deduction in summary