Building large composition tables via axiomatic theories

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Building Large Composition Tables via Axiomatic Theories

The use of composition tables for efficiently representing and reasoning with jointly exhaustive pairwise disjoint sets of dyadic relations, is now well established in the AI literature. Whether typically built from axiomatic theories or from algebraic structures, most tables are built with a single theory in mind. We concentrate upon axiomatic theories for building these tables, and show how by factoring out related, but distinct formal theories (each capable of generating a composition table), large composition tables are easily constructed. This approach contrasts with the general difficulty of extracting out these tables where a parsimonious ontology and minimal number of primitives are used. We illustrate this with the construction of a non-trivial 20x20 composition table from two sub-theories supporting a 6x6 and 8x8 table. The ontological and representational ramifications for general theory building and the value of composition tables are discussed