  We present Scallop, a language which combines the benefits of deep learning
and logical reasoning. Scallop enables users to write a wide range of
neurosymbolic applications and train them in a data- and compute-efficient
manner. It achieves these goals through three key features: 1) a flexible
symbolic representation that is based on the relational data model; 2) a
declarative logic programming language that is based on Datalog and supports
recursion, aggregation, and negation; and 3) a framework for automatic and
efficient differentiable reasoning that is based on the theory of provenance
semirings. We evaluate Scallop on a suite of eight neurosymbolic applications
from the literature. Our evaluation demonstrates that Scallop is capable of
expressing algorithmic reasoning in diverse and challenging AI tasks, provides
a succinct interface for machine learning programmers to integrate logical
domain knowledge, and yields solutions that are comparable or superior to
state-of-the-art models in terms of accuracy. Furthermore, Scallop's solutions
outperform these models in aspects such as runtime and data efficiency,
interpretability, and generalizability.
