Is there a difference between 'inconsistent' and 'contrary'? As far as I understand two statements are inconsistent when they can not both be true. Does 'contrary' have the same definition?
As far as I understand, neither term is perfectly synonymous with the other nor with 'contradictory' (where two variables cannot bear the same truth-value, be it true or false)
So do 'inconsistent', 'contrary', and 'contradictory' each have their own meaning, or are two of those terms mutually synonymous?
Two statements are said to be contradictory if for both statements, the truth of one implies the falsity of the other.
Two statements are said to be contrary if they can both be false, but they cannot both be true.
(I know you used the word "inconsistent" instead of "contradictory", but the latter seems to be the more conventional choice. They're synonymous here though, so take your pick.)
The point you seem to have overlooked about contradictory pairs is that they cannot both be false either.
Inconsistent, in formal logic, is a property of sets of propositions. For instance, the set {A, ¬A} is an inconsistent set.
On the other hand, contrary is a relationship between two propositions, that is to say the proposition A stands in the "contrary" relation to the proposition ¬A.
A set of propositions is inconsistent just in case, for some two propositions in the set, they are contrary to each other.
