Final answer:
Big SQL builds on a Hadoop foundation, providing advanced SQL querying capabilities on top of Hadoop's scalable data storage and processing framework.
Step-by-step explanation:
The type of foundation that Big SQL builds on is C) Hadoop. Big SQL is IBM's advanced SQL engine that runs on top of Hadoop, offering both the scalability and flexibility of Hadoop and the robust querying capabilities of a SQL-based relational database system. It allows users to query data stored in various Hadoop file formats and to combine this data with traditional relational database data. Big SQL's architecture is designed to leverage the distributed processing power of the Hadoop environment while providing familiar SQL syntax and adherence to SQL standards, making it a powerful tool for managing and analyzing big data.