Modus ponens is a rule of inference that is commonly found in many logics where the binary logical connective (sometimes written or ) called logical implication are defined. Informally, it states that
from and , we may infer .
Modus ponens is also called the rule of detachment: the theorem can be “detached” from the theorem provided that is also a theorem.
An example of this rule is the following: From the premisses “It is raining”, and “If it rains, then my laundry will be soaked”, we may draw the conclusion “My laundry will be soaked”.
Two common ways of mathematically denoting modus ponens are the following:
is defined whenever and for some , and
when this is the case, and ;
is not defined otherwise.
If and , then , where is a set of formulas.
To see this, let be a deduction of from , and be a deduction of from . Then is a deduction of from , where is inferred from (which is ) and (which is ) by modus ponens.
|Date of creation||2013-03-22 16:50:48|
|Last modified on||2013-03-22 16:50:48|
|Last modified by||CWoo (3771)|
|Synonym||rule of detachment|
|Synonym||modus ponendo ponens|