Semirings for Probabilistic and Neuro-Symbolic Logic Programming
This work provides a foundational algebraic perspective that unifies probabilistic and neuro-symbolic logic programming, potentially benefiting researchers and practitioners in AI and logic programming by simplifying and generalizing existing methods.
The paper tackles the problem of unifying diverse probabilistic logic programming (PLP) extensions by proposing a common algebraic framework using semirings, where facts are labeled with semiring elements and logical operations are replaced by addition and multiplication, showing that this approach applies to both PLP variations and their execution mechanisms.
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference and learning in probabilistic logic programs. While originally PLP focused on discrete probability, more recent approaches have incorporated continuous distributions as well as neural networks, effectively yielding neural-symbolic methods. We provide a unified algebraic perspective on PLP, showing that many if not most of the extensions of PLP can be cast within a common algebraic logic programming framework, in which facts are labeled with elements of a semiring and disjunction and conjunction are replaced by addition and multiplication. This does not only hold for the PLP variations itself but also for the underlying execution mechanism that is based on (algebraic) model counting.