The Semantics of the Compound Term Composition Algebra

Abstract

In [11], we proposed an algebra with four algebraic operators, whose composition can be used to generate valid compound terms in a given faceted taxonomy in an efficient and flexible manner. The positive operations allow the derivation of valid compound terms through the declaration of a small set of valid compound terms. The negative operations allow the derivation of valid compound terms through the declaration of a small set of invalid compound terms. Here, we formally define the model-theoretic semantics of the operations and the closed-world assumptions adopted in each operation. We prove that our algebra is monotonic with respect to both valid and invalid compound terms, meaning that the valid and invalid compound terms of a subexpression are not invalidated by a larger expression. The importance of this property is demonstrated through an example. We also show that our algebra cannot be directly represented in Description Logics. A metasystem on top of Description Logics is designed to implement our algebra.