×Firstly, lets go through each of the 6 combinations for the 3 members (which one is angel, mortal and demon). For each one, we can easily work out which of the statements can be made by each person. The angel must make the true statement, the mortal any of his options, the demon any but the true statement.
For example, suppose Andra, Bravi, and Comus are A,M,D.
Then Andra must say Comus is a demon, Bravi can say anything, Comus can say Bravi is an angel or demon.
Lets summarise that as follows:

Case A M D:

A says D
B says A,D,M
C says A,D

(which means A says C is a demon, B says A is angel,demon,mortal, C says B is angel,demon).
That leads to the following 6 options for what type of inhabitant each statement mentions:
DAA,DAD,DDA,DDD,DMA,DMD

We do the same thing for the other 5 possibilities:

Case A D M:

A says M
B says D,M
C says A,D,M
MDA,MDD,MDM,MMA,MMD,MMM

Case M A D:

A says D,M
B says M
C says D,M
DMD,DMM,MMD,MMM

Case M D A:

A says D,M
B says A,D
C says D
DAD,DDD,MAD,MDD

Case D M A:

A says D,M
B says A,D,M
C says M
DAM,DDM,DMM,MAM,MDM,MMM

Case D A M:
A says D
B says D
C says A,D,M
DDA,DDD,DDM

Now, lets group all of those possibilities into who comes out to be the thief.

A is thief:
DMD,DMM,MMD,MMM,DAD,DDD,MAD,MDD
B is thief:
DAA,DAD,DDA,DDD,DMA,DMD,DAM,DDM,DMM,MAM,MDM,MMM
C is thief:
MDA,MDD,MDM,MMA,MMD,MMM,DDA,DDD,DDM

Since the judge knows the thief from this information, we remove any triple that occurs in more than one of those three options. That leaves:

A is thief:
MAD
B is thief:
DAA,DMA,DAM,MAM
C is thief:
MDA,MMA

If we're told A says C is a mortal, any of the three could be the thief, so the second logician couldn't work it out. If he said demon, however, B must be the thief.

Therefore B is the thief.