The term 'logically inconsistent' refers to a set of statements such that all of them cannot be true at the same time.

Logical inconstancy is often used in testing to see if a set is consistent. By negating the conclusion, and showing that the new set of statements is logically inconsistent, the original set was logically consistent.

In the following example I use perl style logical notation and the tree method for logical decomposition:

  • -> (therefore)
  • ! (not)
    The conclusion of 'C' has been negated (shown below as 4) !C). If the original set is inconstant, there will be at least one branch of the tree where there is not a logical inconsistency.
    1) A
    2) A -> B  x
    3) B -> C  x
    4) !C
        /  \
       /    \
    5)!A   6)A  (from 2)
       x   7)B  (from 2)
      (1,5) /\
           /  \
          /    \
        8)!B   9)B  (from 3)
          x   10)C  (from 3)
         (7,8)   x

    As can be seen, each branch has a logical inconsistency, and therefore the original set was logically consistent.