Consistency
id:
consistency-170-2575770
title:
Consistency
text:
In classical, deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula φ such that both φ and its negation ¬ φ are elements of the set of consequences of T. Let A be a set of closed sentences and ⟨ A ⟩ the set of closed sentences provable from A under some formal deductive system. The set of axioms A is consistent when there is no formula φ such that φ ∈ ⟨ A ⟩ and ¬ φ ∈ ⟨ A ⟩. A trivial theory is clearly inconsiste
brand slug:
wiki
category slug:
encyclopedia
description:
Non-contradiction of a theory
original url:
https://en.wikipedia.org/wiki/Consistency
date created:
2002-08-25T01:14:35Z
date modified:
2024-08-31T18:16:12Z
main entity:
{"identifier":"Q1319773","url":"https://www.wikidata.org/entity/Q1319773"}
image:
fields total:
13
integrity:
15