In the context of mathematical
logic and more specifically,
Boolean algebra, consistency is an important notion.
A collection of statements is said to be
consistent if the statements can all be
true simultaneously.
A simple way of determining if a (hopefully small) collection of statements is consistent or not is to use a
truth table.
The concept of consistency is important in
refutation strategy, a method of determining the
validity of an argument. In this method, the
conclusion to the proposed argument is negated, then all the statements are checked for consistency. If the argument and the negated conclusion are
mutually inconsistent, then the original conclusion must be valid.