A faceted taxonomy is a set of taxonomies, each describing a given knowledge domain from a different aspect. The indexing of the domain objects is done using compound terms, i.e. conjunctive combinations of terms from the taxonomies. A faceted taxonomy has several advantages over a single taxonomy, including conceptual clarity, compactness, and scalability. A drawback, however, is the cost of identifying compound terms that are invalid, i.e. terms that do not apply to any object of the domain. This need arises both in indexing and retrieval, and involves considerable human effort for specifying the valid compound terms one by one. In this paper, we propose and present in detail an algebra which can be used to specify the set of valid compound terms in an efficient and flexible manner. It works on the basis of the original simple terms of the facets and a small set of positive and/or negative statements. In each algebraic operation, we adopt a closed-world assumption with respect to the declared positive or negative statements. In this paper we elaborate on the properties of the algebraic operators and we describe application and methodological issues.

The notion of context appears in computer science, as well as in several other disciplines, in various forms. In this paper, we present a general framework for representing the notion of context in information modeling. First, we define a context as a set of objects, within which each object has a set of names and possibly a reference: the reference of the object is another context which "hides" detailed information about the object. Then, we introduce the possibility of structuring the contents of a context through the traditional abstraction mechanisms, i.e. classification, generalization, and attribution. We show that, depending on the application, our notion of context can be used as an independent abstraction mechanism, either in an alternative or a complementary capacity with respect to the traditional abstraction mechanisms. We also study the interactions between contextualization and the traditional abstraction mechanisms, as well as the constraints that govern such interactions. Finally, we present a theory for contextualized information bases. The theory includes a set of validity constraints, a model theory, as well as a set of sound and complete inference rules. We show that our core theory can be easily extended to support embedding of particular information models in our contextualization framework.

Although semantic data models provide expressive conceptual

Ontologies and automated reasoning are the building blocks of the Semantic Web initiative. Derivation rules can be included in an ontology to define derived concepts, based on base concepts. For example, rules allow to define the extension of a class or property, based on a complex relation between the extensions of the same or other classes and properties. On the other hand, the inclusion of negative information both in the form of negation-as-failure and explicit negative information is also needed to enable various forms of reasoning. In this paper, we extend RDF graphs with weak and strong negation, as well as derivation rules. The ERDF stable model semantics of the extended framework (Extended RDF) is defined, extending RDF(S) semantics. A distinctive feature of our theory, which is based on Partial Logic, is that both truth and falsity extensions of properties and classes are considered, allowing for truth value gaps. Our framework supports both closed-world and open-world reasoning through the explicit representation of the particular closed-world assumptions and the ERDF ontological categories of total properties and total classes

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