Markov conditions and factorization in logical credal networks1

We examine the recently proposed language of Logical Credal Networks, a powerful representation formalism that combines probabilities and logic. In particular we investigate the consequences of distinct Markov conditions upon their underlying semantics. We introduce the notion of structure for a Logical Credal Network and show that a structure without directed cycles leads to a well-known factorization result. For networks with directed cycles, we discuss the differences between Markov conditions, factorization results, and specification requirements. We consider several scenarios in causal reasoning that can be tackled by the formalism, in particular looking at partial identifiability and cycles.