Reasoning with Examples: Propositional Formulae and Database Dependencies

Abstract

For humans, looking at how concrete examples behave is an intuitive way of deriving conclusions. The drawback with this method is that it does not necessarily give the correct results. However, under certain conditions example-based deduction can be used to obtain a correct and complete inference procedure. This is the case for Boolean formulae (reasoning with models) and for certain types of database integrity constraints (the use of Armstrong relations). We show that these approaches are closely related, and use the relationship to prove new results about the existence and sizes of Armstrong relations for Boolean dependencies. Further, we study the problem of translating between different representations of relational databases, in particular we consider Armstrong relations and Boolean dependencies, and prove some positive results in that context. Finally, we discuss the close relations between the questions of finding keys in relational databases and that of finding abductive explanations.