Towards a Knowledge Level Analysis of Forgetting

Forgetting has been addressed in various areas in KR, including classical logic, logic programming, modal logic, and description logics. Here, we view forgetting as an abstract operator, independent of the underlying logic. We argue that forgetting amounts to a reduction in the signature of a language of a logic, and that the result of forgetting elements of a signature in a theory is the set of logical consequences over the reduced language. This definition offers several advantages. It provides a uniform approach to forgetting, applicable to any logic with a well-defined consequence relation. Obtained results are thus applicable to all subsumed formal systems, and typically are obtained much more straightforwardly. The approach also leads to insights with respect to specific logics: forgetting in first-order logic is somewhat different from the accepted approach; and the definition applied to logic programs yields a new syntax-independent notion of forgetting.