In order to define the contension measure we need to consider three-valued interpretations for propositional logic [Priest:1979]. A three-valued interpretation
on
is a function
where the values
and
correspond to the classical truth values
and
, respectively. The additional truth value
stands for both and is meant to represent a conflicting truth value for a proposition. The function
is extended to arbitrary formulas as shown in the following table
Then, an interpretation satisfies a formula
, denoted by
if either
or
.
The contension inconsistency measure
is defined as
The contension inconsistency measure has been discussed in e.g. [Grant:2011].