Maximum Entropy Reasoning via Model Counting in (Description) Logics that Count

Abstract

In previous work it was shown that the logic ALC^ME,  which extends the description logic (DL) ALC with probabilistic conditionals, has domain-lifted inference. Here, we extend this result from the base logic ALC to two logics that can count, the two-variable fragment C² of first-order logic (FOL) with counting quantifiers, and the DL ALCSCC, which is not a fragment of FOL. As an auxiliary result, we prove that model counting in ALCSCC can be realized in a domain-liftable way.