We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity at all times and another that allows the appearance of nontrivial directed cycles, we provide analytic and simulation results related to the distributions of...

In this work, we consider function-free existential rules extended with nonmonotonic negation under a stable model semantics. We present new acyclicity and stratification conditions that identify a large class of rule sets having finite, unique stable models, and we show how the addition of constraints on the input facts can further extend this class. Checking these conditions is computationall...

We exhibit a two-dimensional, acyclic, Eilenberg–Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π1(X) coincides, up to homotopy, with the W -nullification of X; that is, the natural map X → X+ is homotopy initial among maps X → Y where the based mapping space map∗(W,Y ) is weakly contractible. Furthermore, we describe the ...

In this paper we provide a simple proof of the extension theorem for partial orderings due to Suzumura [1983] when the domain of the partial order is finite. The extension theorem due to Szpilrajn [1930] follows from this theorem. Szpilrajns extension theorem is used to show that an asymmetric binary relation is contained in the asymmetric part of a linear order if and only if it is acyclic. Th...

We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p-complete infinite loop space has a finite number o...

This paper studies the properties of inverse resolution in normal logic programs. The V-operators are known as operations for inductive generalization in definite logic programs. In the presence of negation as failure in a program, however, the V-operators do not work as generalization operations in general and often make a consistent program inconsistent. Moreover, they may destroy the syntact...

State-of-the-art ontology languages are often not sufficiently expressive to accurately represent domains consisting of objects connected in a complex way. As a possible remedy, in our previous work we have proposed an extension of ontology languages with description graphs. In this paper, we extend this formalism by allowing for multiple graphs that can be combined in complex ways, thus obtain...

We study access to temporal data with TEL, a temporal extension of the tractable description logic EL. Our aim is to establish a clear computational complexity landscape for the atomic query answering problem, in terms of both data and combined complexity. Atomic queries in full TEL turn out to be undecidable even in data complexity. Motivated by the negative result, we identify well-behaved ye...

We present four constructions for standard equipment which can be generated for every inductive datatype: case analysis, structural recursion, no confusion, acyclicity. Our constructions follow a two-level approach—they require less work than the standard techniques which inspired them [11, 8]. Moreover, given a suitably heterogeneous notion of equality, they extend without difficulty to induct...

Liveness properties, such as termination, of even the simplest shared-memory concurrent programs under sequential consistency typically require some fairness assumptions about scheduler. Under weak memory models, we observe that standard notions thread are insufficient, and an additional property, which call fairness, is needed. In this paper, propose a uniform definition for can be integrated ...