Merging inheritance hierarchies is an essential task of schema integration as part of the design of a federated database. Based on the formalization of inheritance hierarchies as concept lattices we present an eecient algorithm for deriving an integrated inheritance hierarchy as result of merging two inheritance hierarchies with overlapping extensions and types. Several methods are presented to...

The original justification for the hierarchy of Planck constants came from the indications that Planck constant could have large values in both astrophysical systems involving dark matter and also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also factor spaces of CD and CP2 emerged from consistency conditions. It however seems that TGD actually pr...

An incomplete data cube is a multidimensional hierarchy of aggregate values in which regions of the hierarchy, and the source data from which those regions are derived, are missing. We model an incomplete cube as a collection of complete sub-cubes called cubettes. Each cubette is deened using a precise, simple speciication. The set of cubette speciications concisely characterises the informatio...

Modeling concepts for handling structural data of hierarchically composed complex objects are presented. A complex object is modeled as an hierarchy of interfaces and an im plementation. Objects sharing the same interface at any level have same attributes and attribute values up to that level in the hierarchy. This structuring facilitates storage of multiple object versions and their subsequent...

In this chapter, we consider the application of generalization-based data mining to fuzzy similarity-based object-oriented databases (OODBs). Attribute generalization algorithms have been most commonly applied to relational databases, and we extend these approaches. A key aspect of generalization data mining is the use of a concept hierarchy. The objects of the database are generalized by repla...

The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The full gauge algebra of this hierarchy can be defined independently of a specific theory and is encoded in the embedding tensor that determines the gauge group. ...

The Calculus of Reenements (COR) presented here takes this idea of types as spec-iications and subtyping as reenement and pushes it to an extreme. Types and values are no longer distinguished; in COR we consider a unique hierarchy of objects. A good way to deal with the hierarchy of objects is to structure it as a complete lattice. And if functions are to be considered as rst class citizens in ...

We consider an access control hierarchy based on nested categories. Nested categories are sets of compartments with the property that any two categories are either disjoint or one wholly contains the other. We present a method for representing nested categories by assigning a pair of integers called k-values to each category. Authorization of a user to access an object is determined by comparin...