Abstract We investigate the expressive power of Higher-Order $Datalog^\neg$ under both the well-founded and the stable model semantics, establishing tight connections with complexity classes. We prove that under the well-founded semantics, for all $k\geq 1$ , $(k+1)$ -Order $Datalog^\neg$ captures $k-\textsf {EXP}$ , a result that holds without explicit ordering of the input database. The proof of this fact can be performed either by using the powerful existential predicate variables of the language or by using partially applied relations and relation enumeration. Furthermore, we demonstrate that this expressive power is retained within a stratified fragment of the language. Under the stable model semantics, we show that $(k+1)$ -Order $Datalog^\neg$ captures $\textsf {co}-(k-\textsf {NEXP})$ using cautious reasoning and $k-\textsf {NEXP}$ using brave reasoning, again with analogous results for the stratified fragment augmented with choice rules. Our results establish a hierarchy of expressive power, highlighting an interesting trade-off between order and non-determinism in the context of higher-order logic programing: increasing the order of programs under the well-founded semantics can surpass the expressive power of lower-order programs under the stable model semantics.

As RDF becomes more widely established and the amount of linked data is rapidly increasing, the efficient querying of large amount of data becomes a significant challenge. In this paper, we propose a family of algorithms for querying large amount of linked data in a distributed manner. These query evaluation algorithms are independent of the way the data is stored, as well as of the particular implementation of the query evaluation. We then use the MapReduce paradigm to present a distributed implementation of these algorithms and experimentally evaluate them, although the algorithms could be straightforwardly translated into other distributed processing frameworks. We also investigate and propose multiple query decomposition approaches of Basic Graph Patterns (subclass of SPARQL queries) that are used to improve the overall performance of the distributed query answering . A deep analysis of the effectiveness of these decomposition algorithms is also provided.

Abstract Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. As a result, certain properties of programs appear non-trivial to formalize in purely logical terms. For example, the current characterization of strong equivalence for LPODs, does not coincide with logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence for LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs, a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs.

Abstract A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases (Papadimitriou 1985; Grädel 1992; Vardi 1982; Immerman 1986; Leivant 1989). In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate that on ordered databases, for all k ≥ 2, k-order Datalog captures (k − 1)-EXPTIME. This result suggests that higher-order extensions of Datalog possess superior expressive power and they are worthwhile of further investigation both in theory and in practice.

Abstract. We define notions of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal language is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued ac-cessibility relation. We investigate the correct notion of bisimulation in this context: we define two variants of bisimulation relations and derive relative (to a truth value) modal equivalence results for bisimilar states. We further investigate game semantics for our bisimulation, Hennessy-Milner classes and other relevant properties. If the underlying algebra H is finite, Heyting-valued modal models can be equivalently reformu-lated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw from this formulation, which is of independent interest to Knowledge Representation applications.

In all-optical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength assignment. Here we study the problem for rings under both the undirected and the directed settings, corresponding to symmetric and one-way communication respectively. The problem in graph-theoretic terms can be formulated as the maximum routing and path coloring problem. We present a chain-and-matching technique for routing requests and coloring the corresponding paths which gives constant approximations for both the undirected and the directed cases. For the undirected problem we obtain a 2/3-approximation algorithm; this corresponds to a considerable increase in the number of satisfied requests compared to the best known algorithm so far, due to Wan and Liu (1998), that achieves a 1 - 1/e ratio using iteratively a maximum edge-disjoint paths algorithm. For the directed case, we also introduce a balanced matching method which, combined with the chain-and-matching technique, gives a 7/11-approximation algorithm. This algorithm also improves upon the (1 $1/e)-approximation algorithm that can be obtained by extending the iterative method of Wan and Liu.