  The recommendation system is not only a problem of inductive statistics from
data but also a cognitive task that requires reasoning ability. The most
advanced graph neural networks have been widely used in recommendation systems
because they can capture implicit structured information from graph-structured
data. However, like most neural network algorithms, they only learn matching
patterns from a perception perspective. Some researchers use user behavior for
logic reasoning to achieve recommendation prediction from the perspective of
cognitive reasoning, but this kind of reasoning is a local one and ignores
implicit information on a global scale. In this work, we combine the advantages
of graph neural networks and propositional logic operations to construct a
neuro-symbolic recommendation model with both global implicit reasoning ability
and local explicit logic reasoning ability. We first build an item-item graph
based on the principle of adjacent interaction and use graph neural networks to
capture implicit information in global data. Then we transform user behavior
into propositional logic expressions to achieve recommendations from the
perspective of cognitive reasoning. Extensive experiments on five public
datasets show that our proposed model outperforms several state-of-the-art
methods, source code is avaliable at [https://github.com/hanzo2020/GNNLR].
