Sparse term encoding for dynamic taxonomies

Abstract

Many domains of knowledge are related by a partial order. In Conceptual Graphs, both the type lattice and the generalization hierarchy exhibit a partial order structure. In many practical systems, the vast amount of taxonomic knowledge necessitates encoding that knowledge in a form that facilitates fast answers to taxonomic operations, such as computing greatest lower bounds. A number of researchers have proposed encoding algorithms and implementations. These techniques each have advantages and disadvantages, in terms of the space and time efficiency of the resulting encoding, the efficiency of the encoding algorithm (which is particularly important for dynamic knowledge) and the operations supported. Our main goal in this paper is to propose sparse logical terms as a universal encoding implementation. We show how sparse terms generalize bit-vectors, logical terms, integer vectors and interval sets, all of which have been used for encoding. As such, the algorithms developed for these implementations are directly applicable to sparse terms. We also argue that simple encoding algorithms (e.g. transitive closure and compact) implemented with sparse terms provide the efficiency and flexibility required for dynamic orders. We justify this claim using encoding results for theoretical and empirical partial orders.

This research was supported by the author's ECO-Research Doctoral Fellowship and by V. Dahl's NSERC Research Grant 31-611024 and NSERC Infrastructure and Equipment Grant given to the Logic and Functional Programming Lab. We are also thankful for the facilities provided by the School of Computing Science at SFU.