  Users may demand recommendations with highly personalized requirements
involving logical operations, e.g., the intersection of two requirements, where
such requirements naturally form structured logical queries on knowledge graphs
(KGs). To date, existing recommender systems lack the capability to tackle
users' complex logical requirements. In this work, we formulate the problem of
recommendation with users' logical requirements (LogicRec) and construct
benchmark datasets for LogicRec. Furthermore, we propose an initial solution
for LogicRec based on logical requirement retrieval and user preference
retrieval, where we face two challenges. First, KGs are incomplete in nature.
Therefore, there are always missing true facts, which entails that the answers
to logical requirements can not be completely found in KGs. In this case, item
selection based on the answers to logical queries is not applicable. We thus
resort to logical query embedding (LQE) to jointly infer missing facts and
retrieve items based on logical requirements. Second, answer sets are
under-exploited. Existing LQE methods can only deal with query-answer pairs,
where queries in our case are the intersected user preferences and logical
requirements. However, the logical requirements and user preferences have
different answer sets, offering us richer knowledge about the requirements and
preferences by providing requirement-item and preference-item pairs. Thus, we
design a multi-task knowledge-sharing mechanism to exploit these answer sets
collectively. Extensive experimental results demonstrate the significance of
the LogicRec task and the effectiveness of our proposed method.
