Reduced Implicate Tries with Updates

The reduced implicate trie, introduced in Murray and Rosenthal (2005, Vol. 3702 of Lecture Notes in Artifical Intelligence, pp. 231-244), is a data structure that may be used as a target language for knowledge compilation. It has the property that, even when large, it guarantees fast response to queries. Specifically, a query can be processed in time linear in the size of the query regardless of the size of the compiled knowledge base. The knowledge compilation paradigm typically assumes that the 'intractable part' of the processing be done once, during compilation. This assumption could render updating the knowledge base infeasible if recompilation is required. The ability to install updates without recompilation may therefore considerably widen applicability. In this article, several update operations not requiring recompilation are developed. These include disjunction, substitution of truth constants, conjunction with unit clauses, reordering of variables and conjunction with arbitrary clauses.