Toward a Knowledge Level Analysis of Forgetting

ABSTRACT. Forgetting has been addressed in different areas of Knowledge Representation, including classical logic, logic programming, modal logic, and description logics. In this paper, we present an account of forgetting as an abstract belief change operator, independent of an underlying logic. We argue that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The central definition is simple: the result of forgetting signature $\sigma$ in a theory is simply the set of logical consequences over the reduced language. This definition offers various advantages. It provides a uniform approach to forgetting, with a single definition applicable to any logic with a well-defined consequence relation. Results obtained are obviously applicable to all subsumed formal systems, and in fact many results are obtained much more straightforwardly. We argue that the perspective provided by the approach leads to simpler approaches to computing forgetting in specific logics. This view also leads to insights with respect to specific logics: forgetting in first-order logic is somewhat different from the accepted approach; the definition relativised to logic programs yields a new syntax-independent notion of forgetting; in modal logic the specification is simpler. Moreover, the obtained perspective clarifies the relation between forgetting and the belief change operation of contraction.