A Four-Valued Logic for Rough Set-Like Approximate Reasoning

This paper extends the basic rough set formalism introduced by Pawlak [1] to a rule-based knowledge representation language, called Rough Datalog, where rough sets are represented by predicates and described by finite sets of rules. The rules allow us to express background knowledge involving rough concepts and to reason in such a knowledge base. The semantics of the new language is based on a four-valued logic, where in addition to the usual values True and False, we also have the values Boundary, representing uncertainty, and Unknown corresponding to the lack of information. The semantics of our language is based on a truth ordering different from the one used in the well-known Belnap logic [2, 3] and we show why Belnap logic does not properly reflect natural intuitions related to our approach. The declarative semantics and operational semantics of the language are described. Finally, the paper outlines a query language for reasoning about rough concepts.