Compound Term Composition Algebra: The Semantics

The Compound Term Composition Algebra (CTCA) is an algebra with four algebraic operators, whose composition can be used to specify the meaningful (valid) compound terms (conjunctions of terms) in a given faceted taxonomy in an e±cient 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. In this paper, we formally define the model-theoretic semantics of the operations and the closed-world assumptions adopted in each operation. We prove that CTCA 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. We show that CTCA cannot be directly represented in Description Logics. However, we show how we could design a metasystem on top of Description Logics in order to implement this algebra.