### Abstract

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.

Original language | English |
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Pages (from-to) | 58-84 |

Number of pages | 27 |

Journal | Journal on Data Semantics |

Volume | 3360 |

Publication status | Published - 2004 |

### Keywords

- Faceted Taxonomies
- Description Logics
- Semantics

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## Cite this

Tzitzikas, Y., Analti, A., & Spyratos, N. (2004). Compound Term Composition Algebra: The Semantics.

*Journal on Data Semantics*,*3360*, 58-84.