# Markov Conditions and Factorization in Logical Credal Networks

## TL;DR

This paper explores the properties of Logical Credal Networks, focusing on how different Markov conditions affect their structure, factorization, and specification, especially in networks with and without cycles.

## Contribution

It introduces the concept of structure in Logical Credal Networks and analyzes the impact of Markov conditions on factorization and network properties.

## Key findings

- Acyclic structures lead to known factorization results.
- Differences between Markov conditions in cyclic networks are analyzed.
- The paper clarifies specification requirements for various network structures.

## Abstract

We examine the recently proposed language of Logical Credal Networks, in particular investigating the consequences of various Markov conditions. 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 analyze the differences between Markov conditions, factorization results, and specification requirements.