Seymour Ginsburg coauthored the 1969 studies of the abstract family of languages framework with Sheila Greibach and John Hopcroft. This approach compares formal-language classes through closure properties instead of one particular grammar or machine presentation.[ref]
Studies in Abstract Families of Languages by Seymour Ginsburg and others. Abstract families of languages, pp.1–32
For example, closure under intersection with regular languages permits restricting an existing language by a finite-state filter. That property is weaker than closure under arbitrary intersections: two context-free languages can have a non-context-free intersection. Stating the allowed operation precisely keeps a shared abstract framework from incorrectly identifying different language classes.
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