  Logical probability theory was developed as a quantitative measure based on
Boole's logic of subsets. But information theory was developed into a mature
theory by Claude Shannon with no such connection to logic. A recent development
in logic changes this situation. In category theory, the notion of a subset is
dual to the notion of a quotient set or partition, and recently the logic of
partitions has been developed in a parallel relationship to the Boolean logic
of subsets (subset logic is usually mis-specified as the special case of
propositional logic). What then is the quantitative measure based on partition
logic in the same sense that logical probability theory is based on subset
logic? It is a measure of information that is named "logical entropy" in view
of that logical basis. This paper develops the notion of logical entropy and
the basic notions of the resulting logical information theory. Then an
extensive comparison is made with the corresponding notions based on Shannon
entropy.
