  This papers develops a logical language for representing probabilistic causal
laws. Our interest in such a language is twofold. First, it can be motivated as
a fundamental study of the representation of causal knowledge. Causality has an
inherent dynamic aspect, which has been studied at the semantical level by
Shafer in his framework of probability trees. In such a dynamic context, where
the evolution of a domain over time is considered, the idea of a causal law as
something which guides this evolution is quite natural. In our formalization, a
set of probabilistic causal laws can be used to represent a class of
probability trees in a concise, flexible and modular way. In this way, our work
extends Shafer's by offering a convenient logical representation for his
semantical objects.
  Second, this language also has relevance for the area of probabilistic logic
programming. In particular, we prove that the formal semantics of a theory in
our language can be equivalently defined as a probability distribution over the
well-founded models of certain logic programs, rendering it formally quite
similar to existing languages such as ICL or PRISM. Because we can motivate and
explain our language in a completely self-contained way as a representation of
probabilistic causal laws, this provides a new way of explaining the intuitions
behind such probabilistic logic programs: we can say precisely which knowledge
such a program expresses, in terms that are equally understandable by a
non-logician. Moreover, we also obtain an additional piece of knowledge
representation methodology for probabilistic logic programs, by showing how
they can express probabilistic causal laws.
