Unification in the Description Logic EL

The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.Comment: 31page

Terminological cycles and the ropositional μ-calculus

We investigate terminological cycles in the terminological standard logic mathcal{ALC} with the only restriction that recursively defined concepts must occur in their definition positively. This restriction, called syntactic monotonicity, ensures the existence of least and greatest fixpoint models. It turns out that as far as syntactically monotone terminologies of mathcal{ALC} are concerned, the descriptive semantics as well as the least and greatest fixpoint semantics do not differ in the computational complexity of the corresponding subsumption relation. In fact, we prove that in each case subsumption is complete for deterministic exponential time. We then show that the expressive power of finite sets of syntactically monotone terminologies of mathcal{ALC} is the very same for the least and the greatest fixpoint semantics and, moreover, in both cases they are strictly stronger in expressive power than mathcal{ALC} augmented by regular role expressions. These results are obtained by a direct correspondence to the so-called propositional mu-calculus which allows to express least and greatest fixpoints explicitly. We propose ALC augmented by the fixpoint operators of the mu-calculus as a unifying framework for all three kinds of semantics

Taking Sides: Marriage networks and Dravidian Kinship in Lowland South America

Dual organization is a unifying concept underlying seemingly dissimilar alliance structures. We explore this idea with reference to lowland South America where dual organization is common. We have chosen, however, to place primary emphasis on the patterning of actual marriage networks. Our aim is to identify the invariant properties of such networks and, in the light of these findings, to reconsider the relationship between marriage network structure and other, categorical or jural features of social organization: kinship terminologies, descent principles, marriage rules, etc. As a means to this end, we develop the concept of matrimonial "sidedness". In doing so, we derive new results concerning dual organization and a new understanding of dravidianate systems. This analysis is based, on the one hand, on published genealogical data concerning the Makuna (Arhem 1981), the Pakaa-Nova (Vilaca 1992), the Yanomamo (Chagnon 1974), the Trio (Riviere 1969), the Parakana (Fausto 1990), the Waimiri-Artroari (Ferreira da Silva 1993), the Guahibo (Metzger 1968), the Shavante (Maybury-Lewis 1967) and the Suya (Seeger 1981), and on the other hand, on Hornborg's (1988) comparative study of 48 lowland South American societies

The first-order theory of lexicographic path orderings is undecidable

We show, under some assumption on the signature, that the *This formula not viewable on a Text-Browser* fragment of the theory of any lexicographic path ordering is undecidable. This applies to partial and to total precedences. Our result implies in particular that the simplification rule of ordered completion is undecidable

LAYLAB : a constraint-based layout manager for multimedia presentations

When developing advanced intelligent user interfaces composing text, graphics, animation, hypermedia etc., the question of automatically designing the graphical layout of such multimedia presentations in an appropriate format plays a crucial role. This paper introduces the task, the functionality and the architecture of the constraint-based multimedia layout manager LayLab