Existential rules, i.e. Datalog extended with existential quantifiers in rule heads, are currently studied under a variety of names such as Datalog+/–, ∀∃rules, and tuple-generating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language fragments for which query answering is decidable. This paper extends and consolidates two of the main appro...

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint and are not well-suited to general purpose optimization packages for their solution...

We study restricted improvement cycles (ri-cycles) in finite positional n-person games with perfect information modeled by directed graphs (digraphs) that may contain directed cycles (di-cycles). We obtain criteria of restricted improvement acyclicity (ri-acyclicity) in two cases: for n = 2 and for acyclic digraphs. We also provide several examples that outline the limits of these criteria and ...

We show that the propositional model counting problem #SAT for CNFformulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore,...

Abstract Multipath cohomology is a theory for directed graphs, which defined using the path poset. The aim of this paper to investigate combinatorial properties posets and provide computational tools multipath cohomology. In particular, we develop acyclicity criteria computations groups oriented linear graphs. We further interpret poset as face simplicial complex, realisability problems.

In this work we study preference systems suitable for the Peer-to-Peer paradigm. Most of them fall in one of the three following categories: global, symmetric and complementary. All these systems share an acyclicity property. As a consequence, they admit a stable (or Pareto e cient) con guration, where no participant can collaborate with better partners than their current ones. We analyze the r...

Causal networks are graphically represented by directed acyclic graphs (DAGs). Learning causal networks from data is a challenging problem due to the size of the space of DAGs, the acyclicity constraint placed on the graphical structures, and the presence of equivalence classes. In this article, we develop an L1-penalized likelihood approach to estimate the structure of causal Gaussian networks...

Existential rules have been proposed for representing ontological knowledge, specifically in the context of OntologyBased Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. Several variants of the chase have been proposed. In the first part of this paper...

In non-partitional models of knowledge with objective and subjective state spaces, the issue of self-consistency arises. The present paper defines a multigraph Gj for each player j, and also a global multigraph G. The posteriors of player j are self-consistent if and only if all cycle equations associated with cycles in Gj are satisfied. Similarly, the posteriors of all players are consistent w...