We investigate the computational complexity of two decision problems on hypergraphs, namely the Spanning Acyclic Subhypergraph problem and the Maximal Acyclic Subhypergraph problem. The former is the existence of an acyclic subhypergraph such that each vertex of the input hypergraph is contained in at least one hyperedge of the subhypergraph. The latter is the existence of an acyclic subhypergr...

Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity...

Acyclicity is a recurring property of solutions to many important combinatorial problems. In this work we study embeddings of specialized acyclicity constraints in the satisfiability problem of the classical propositional logic (SAT). We propose an embedding of directed graphs in SAT, with arcs labelled with propositional variables, and an extended SAT problem in which all clauses have to be sa...

Rules that allow existential quantifiers in the head (conclusion) have been studied extensively in knowledge representation, databases, and logic programming (in the related form of logic programs with function symbols). In general, it is not decidable if a set of such rules admits a finite model, but a number of sufficient conditions have been proposed to detect situations where this is the ca...

The notions of γ and β-acyclicity are two classic generalizations of the acyclicity of graphs to hypergraphs. They satisfy the property that, if a hypergraph is γ-acyclic then it is β-acyclic, and the reverse is false. We give some new properties concerning these notions. First we show that we can strictly insert another notion of acyclicity between them, namely the fact of having a join tree w...

Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity...