Bayesian networks (BNs) are a probabilistic graphical model widely used for
representing expert knowledge and reasoning under uncertainty. Traditionally,
they are based on directed acyclic graphs that capture dependencies between
random variables. However, directed cycles can naturally arise when
cross-dependencies between random variables exist, e.g., for modeling feedback
loops. Existing methods to deal with such cross-dependencies usually rely on
reductions to BNs without cycles. These approaches are fragile to generalize,
since their justifications are intermingled with additional knowledge about the
application context. In this paper, we present a foundational study regarding
semantics for cyclic BNs that are generic and conservatively extend the
cycle-free setting. First, we propose constraint-based semantics that specify
requirements for full joint distributions over a BN to be consistent with the
local conditional probabilities and independencies. Second, two kinds of limit
semantics that formalize infinite unfolding approaches are introduced and shown
to be computable by a Markov chain construction.

本文提出基于约束和限制两种语义的循环贝叶斯网络的研究，并证明这两种语义可以通过马尔可夫链构造来计算。