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In the context of my Constraint Database class, we talk about the specific instances or interpretations of a boolean algebra (with AND, OR, NOT, TRUE, FALSE, etc) and also about a uninterpreted or free boolean algebra. You can think of it as being an axiomatic approach to a boolean algebra where in proofs you are restricted to using the axioms not the specific meaning of the + or * operators which may be anything as long as they satisfy the properties of an algebra.
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