  Complementary recommendation gains increasing attention in e-commerce since
it expedites the process of finding frequently-bought-with products for users
in their shopping journey. Therefore, learning the product representation that
can reflect this complementary relationship plays a central role in modern
recommender systems. In this work, we propose a logical reasoning network,
LOGIREC, to effectively learn embeddings of products as well as various
transformations (projection, intersection, negation) between them. LOGIREC is
capable of capturing the asymmetric complementary relationship between products
and seamlessly extending to high-order recommendations where more comprehensive
and meaningful complementary relationship is learned for a query set of
products. Finally, we further propose a hybrid network that is jointly
optimized for learning a more generic product representation. We demonstrate
the effectiveness of our LOGIREC on multiple public real-world datasets in
terms of various ranking-based metrics under both low-order and high-order
recommendation scenarios.
