RACE [3] is a successor of HAM-ALC [5, 2]. Based on sound and complete algorithms RACE currently implements TBox and ABox reasoning for the description logic ALCNHR+ [4] that supports number restrictions, role hierarchies, and transitively closed roles. Note that this DL implies general concept inclusions as a language feature. RACE accepts TBoxes and ABoxes in the KRSS syntax with appropriate ...

1 Regular Languages and Logic 3 1.1 Regular Languages and Finite Automata . . . . . . . . . 3 1.2 First-Orderand Monadic-Second-Order-Logic . . . . . 5 2 Other Equivalent Representations 9 2.1 Two-way Finite Automata . . . . . . . . . . . . . . . . . 9 2.2 First Order Logic with Transitive Closure . . . . . . . . 13 3 Two-Way Multihead Automata 17 4 k-ary Transitive Closure 26 5 Tree Walking Au...

Transitive closure operation is one of the most useful new operations in deductive database systems. When it is added to conventional relational database systems, most practical problems with recursion can be coped with. Therefore, efficient processing of transitive closure is an important task in deductive database systems. Transitive closure operation can be divided into total closure and que...

for all x, y, z ∈ L. (So we do not require the dual arrow nor the associativity of .) In other words, the actions − y, y ( − : L→ L, for any fixed y ∈ L, provide a Galois connection on L. The Galois connection is also completely determined by the partial isomorphism between fixpoints of closure mapping y ( (− y) and coclosure mapping (y ( −) y. Thus we can restrict ,( to partial operations ·,→ ...

A recent problem in dynamics is to determine whether an attractor Λ of a C flow X is C robust transitive. By an attractor we mean a transitive set to which all positive orbits close to it converge. An attractor is C robust transitive (or C robust for short) if it has a neighborhood U such that the set ⋂ t>0 Yt(U) is transitive for every flow Y that is C r close to X. We give sufficient conditio...

In this work, we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than 1013 in absolute value. For each field in the list we give its discriminant, the discriminant of its subfield, a relative polynomial generating the field over one of its subfields, the corresponding polynomial over Q, and the Galois group of ...

This paper is motivated by the desire to evaluate certain classical convexity invariants (specifically, the Helly and Radon numbers) in the context of transitive closure of arcs in the complete digraph. To do so, it is necessary to establish several new Turán type results for digraphs and characterize the associated extremal digraphs. In the case of the Radon number, we establish the following ...

A topic that is currently inspiring a lot of research is parallel (distributed) computation of transitive closure queries. In 10] the disconnection set approach has been introduced as an eeective strategy for such a computation. It involves reformulating a transitive closure query on a relation into a number of transitive closure queries on smaller fragments; these queries can then execute inde...

In this paper we propose clustering methods based on weighted quasiarithmetic means of T -transitive fuzzy relations. We first generate a T -transitive closure R from a proximity relation R based on a max-T composition and produce a T -transitive lower approximation or opening RT from the proximity relation R through the residuation operator. We then aggregate a new T -indistinguishability fuzz...

We explore the possibility of evaluating single-rule Datalog programs eeciently and with logarithmic work space by a natural extension of the Floyd-Warshall algorithm for transitive closure. We characterize exactly the single rule chain programs that can be so evaluated: they are rather modest generalizations of the transitive closure. The proof relies on an interesting language-theoretic conce...