In all my years with database systems, I have never heard of the term "problem space". I even went back to my old textbooks from when I studied database systems in graduate school and we never used that term there either. On the web, I did find the term "problem space" defined here:
From the above website, basically the problem space is the list of rules, tasks, and outcomes needed to solve a problem. Moving this definition into the database world, I would add that the problem space also contains the entities and attributes needed to help solve the problem, or solve the business needs the database needs to support.
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