66 research outputs found
Extensions of Simple Conceptual Graphs: the Complexity of Rules and Constraints
Simple conceptual graphs are considered as the kernel of most knowledge
representation formalisms built upon Sowa's model. Reasoning in this model can
be expressed by a graph homomorphism called projection, whose semantics is
usually given in terms of positive, conjunctive, existential FOL. We present
here a family of extensions of this model, based on rules and constraints,
keeping graph homomorphism as the basic operation. We focus on the formal
definitions of the different models obtained, including their operational
semantics and relationships with FOL, and we analyze the decidability and
complexity of the associated problems (consistency and deduction). As soon as
rules are involved in reasonings, these problems are not decidable, but we
exhibit a condition under which they fall in the polynomial hierarchy. These
results extend and complete the ones already published by the authors. Moreover
we systematically study the complexity of some particular cases obtained by
restricting the form of constraints and/or rules
On the k-Boundedness for Existential Rules
The chase is a fundamental tool for existential rules. Several chase variants
are known, which differ on how they handle redundancies possibly caused by the
introduction of nulls. Given a chase variant, the halting problem takes as
input a set of existential rules and asks if this set of rules ensures the
termination of the chase for any factbase. It is well-known that this problem
is undecidable for all known chase variants. The related problem of boundedness
asks if a given set of existential rules is bounded, i.e., whether there is a
predefined upper bound on the number of (breadth-first) steps of the chase,
independently from any factbase. This problem is already undecidable in the
specific case of datalog rules. However, knowing that a set of rules is bounded
for some chase variant does not help much in practice if the bound is unknown.
Hence, in this paper, we investigate the decidability of the k-boundedness
problem, which asks whether a given set of rules is bounded by an integer k. We
prove that k-boundedness is decidable for three chase variants, namely the
oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201
RDF to Conceptual Graphs Translations
International audienceIn this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and complete from a reasoning view point but is not visual nor a representation in the spirit of Conceptual Graphs (CGs). The second translation has the advantage of being natural and fully exploiting the CG features, but, on the other hand it does not apply to the whole RDF(S). We aim this paper as a preliminary report of ongoing work looking in detail at different pro and the cons of each approach
Query rewriting under linear EL knowledge bases
With the adoption of the recent SPARQL 1.1 standard, RDF databases are capable of directly answering more expressive queries than simple conjunctive queries. In this paper we exploit such capabilities to answer conjunctive queries (CQs) under ontologies expressed in the description logic called linear EL-lin, a restricted form of EL. In particular, we show a query answering algorithm that rewrites a given CQ into a conjunctive regular path query (CRPQ) which, evaluated on the given instance, returns the correct answer. Our technique is based on the representation of infinite unions of CQs by non-deterministic finite-state automata. Our results achieve optimal data complexity, as well as producing rewritings straightforwardly implementable in SPARQL 1.1
On the succinctness of query rewriting over shallow ontologies
We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existential rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of conjunctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP �is included in P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable
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