  A complex logic query in a knowledge graph refers to a query expressed in
logic form that conveys a complex meaning, such as where did the Canadian
Turing award winner graduate from? Knowledge graph reasoning-based
applications, such as dialogue systems and interactive search engines, rely on
the ability to answer complex logic queries as a fundamental task. In most
knowledge graphs, edges are typically used to either describe the relationships
between entities or their associated attribute values. An attribute value can
be in categorical or numerical format, such as dates, years, sizes, etc.
However, existing complex query answering (CQA) methods simply treat numerical
values in the same way as they treat entities. This can lead to difficulties in
answering certain queries, such as which Australian Pulitzer award winner is
born before 1927, and which drug is a pain reliever and has fewer side effects
than Paracetamol. In this work, inspired by the recent advances in numerical
encoding and knowledge graph reasoning, we propose numerical complex query
answering. In this task, we introduce new numerical variables and operations to
describe queries involving numerical attribute values. To address the
difference between entities and numerical values, we also propose the framework
of Number Reasoning Network (NRN) for alternatively encoding entities and
numerical values into separate encoding structures. During the numerical
encoding process, NRN employs a parameterized density function to encode the
distribution of numerical values. During the entity encoding process, NRN uses
established query encoding methods for the original CQA problem. Experimental
results show that NRN consistently improves various query encoding methods on
three different knowledge graphs and achieves state-of-the-art results.
