Relational data modeling can often be restrictive as it provides no direct facility for modeling polymorphic types, reified relations, multi-valued attributes, and other common high-level structures in data. This creates many challenges in data modeling and engineering tasks, and has led to the rise of more flexible NoSQL databases, such as graph and document databases. In the absence of structured schemas, however, we can neither express nor validate the intention of data models, making long-term maintenance of databases substantially more difficult. To resolve this dilemma, we argue that, parallel to the role of classical predicate logic for relational algebra, contemporary foundations of mathematics rooted in type theory can guide us in the development of powerful new high-level data models and query languages. To this end, we introduce a new polymorphic entity-relation-attribute (PERA) data model, grounded in type-theoretic principles and accessible through classical conceptual modeling, with a near-natural query language: TypeQL. We illustrate the syntax of TypeQL as well as its denotation in the PERA model, formalize our model as an algebraic theory with dependent types, and describe its stratified semantics.

Over the past decades, data modeling has become a highly diversified discipline with many competing paradigms emerging across various application domains. We argue that higher levels of abstraction including, in particular, the integration of high-level programming and reasoning techniques, will pave the way forward for future knowledge management systems. As a programmatic foundation for this endeavor, we will discuss a novel type theoretical modeling and reasoning paradigm, which aims to strike a powerful balance between what can be naturally semantically modeled and what can be practically implemented. TypeQL is a multi-purpose database language rooted in these foundations: it is designed around the expressivity of natural language and backed by type theoretical principles. This rigorous high-level approach to database language reduces development and maintenance loads, preventing hard to spot data integrity and logic errors through its underlying type system, while also providing a unifying toolset for a large class of domain-specific applications ranging from querying connected data in knowledge graphs for drug discovery to reasoning and adaptive decision making in cognitive robotics.