In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no formula φ {\displaystyle \varphi } such that both φ {\displaystyle \varphi } and its negation ¬ φ {\displaystyle \lnot \varphi } are elements of the set of consequences of T {\displaystyle T} .
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no formula φ {\displaystyle \varphi } such that both φ {\displaystyle \varphi } and its negation ¬ φ {\displaystyle \lnot \varphi } are elements of the set of consequences of T {\displaystyle T} .
Source: Wikipedia "Consistency" · CC BY-SA 4.0
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