Independence of premise
id:
independence-of-premise-171-11742039
title:
Independence of premise
text:
In proof theory and constructive mathematics, the principle of independence of premise (IP) states that if φ and ∃x θ are sentences in a formal theory and φ → ∃x θ is provable, then ∃x is provable. Here x cannot be a free variable of φ, while θ can be a predicate depending on it. The main application of the principle is in the study of intuitionistic logic, where the principle is not generally valid. Its crucial equivalent special case is discussed below.
The principle is valid in classical logi
brand slug:
wiki
category slug:
encyclopedia
description:
Mathematical principle largely used in proof theory and constructive Mathematics
original url:
https://en.wikipedia.org/wiki/Independence_of_premise
date created:
2009-05-17T13:14:45Z
date modified:
2024-09-01T11:04:00Z
main entity:
{"identifier":"Q6016278","url":"https://www.wikidata.org/entity/Q6016278"}
image:
fields total:
13
integrity:
15