We present a new tableaux calculus deciding the ABox consistency problem for the expressive description logic ALCNHR+ . Prominent language features of ALCNHR+ are number restrictions, role hierarchies, transitively closed roles, and generalized concept inclusions. The ABox description logic system RACE is based on the calculus for ALCNHR+ .

Let I denote an R+-primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Frobenius powers I [q] of I, q = p, in terms of the minimal slope of the top-dimensional syzygy bundle on the projective variety ProjR. This provides an inclusion bound for tight closure. In the same manner we give a line...

We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on nite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTC-query is bounded and therefore rst order expressible. On the other hand there are simple (FO + pos TC) queries on these cla...

Semigroups with an additional unary operation called a (right) closure are investigated. These “closure semigroups” may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformat...

Improving and maintaining data quality has become a critical issue for many companies and organizations because poor data degrades organizational performance whereas quality data results in cost saving and customer satisfaction. Activities such as identifying and removing ”duplicate” database records from a single database, and correlating records, which identify the same real world ”entity”, f...

Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min{mn, n2.38}) time, where n is the number of nodes and m the number of edges in the graph. We present an O(m) time ...

We consider a model for representing innnite-state and para-meterized systems, in which states are represented as strings over a nite alphabet. Actions are transformations on strings, in which the change can be characterized by an arbitrary nite-state transducer. This program model is able to represent programs operating on a variety of data structures, such as queues, stacks, integers, and sys...

We formulate an infinitary proof system for transitive closure logic, which is the logic obtained by augmenting first-order logics with a transitive closure operator. Our system is an infinite descent-style counterpart to the existing (explicit induction) proof system for the logic. We show that, as for similar systems for first order logic with inductive definitions, our infinitary system is c...

The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...