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

A Pure Graph-Based Solution to the SCG-1 Initiative

Abstract. This paper answers the SCG-1 initiative. The room allocation problem provided has been solved in a generic and automatic way. The solution is based on a totally declarative formal model. Basic constructs are simple graphs and the fundamental operation for doing reasonings is the graph morphism known as projection. The other formal constructs are rules and constraints defined in terms of simple graphs. The modeling framework built upon the formal model allows one to describe a problem with asserted facts, rules representing implicit knowledge about the do-main, validity constraints and rules transforming the world. A prototype implementing this framework has been built upon the tool CoGITaNT. It has been used to test our modelization of the room allocation problem.

Querying Visible and Invisible Information

We provide a wide-ranging study of the scenario where a subset of the relations in the schema are visible - that is, their complete contents are known - while the remaining relations are invisible. We also have integrity constraints (invariants given by logical sentences) which may relate the visible relations to the invisible ones. We want to determine which information about a query (a positive existential sentence) can be inferred from the visible instance and the constraints. We consider both positive and negative query information, that is, whether the query or its negation holds. We consider the instance-level version of the problem, where both the query and the visible instance are given, as well as the schema-level version, where we want to know whether truth or falsity of the query can be inferred in some instance of the schema

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

Requirements modelling and formal analysis using graph operations

The increasing complexity of enterprise systems requires a more advanced analysis of the representation of services expected than is currently possible. Consequently, the specification stage, which could be facilitated by formal verification, becomes very important to the system life-cycle. This paper presents a formal modelling approach, which may be used in order to better represent the reality of the system and to verify the awaited or existing system’s properties, taking into account the environmental characteristics. For that, we firstly propose a formalization process based upon properties specification, and secondly we use Conceptual Graphs operations to develop reasoning mechanisms of verifying requirements statements. The graphic visualization of these reasoning enables us to correctly capture the system specifications by making it easier to determine if desired properties hold. It is applied to the field of Enterprise modelling

GUN: An Efficient Execution Strategy for Querying the Web of Data

International audienceLocal-As-View (LAV) mediators provide a uniform interface to a federation of heterogeneous data sources, attempting to execute queries against the federation. LAV mediators rely on query rewriters to translate mediator queries into equivalent queries on the federated data sources. The query rewriting problem in LAV mediators has shown to be NP-complete, and there may be an exponential number of rewritings, making unfeasible the execution or even generation of all the rewritings for some queries. The complexity of this problem can be particularly impacted when queries and data sources are described using SPARQL conjunctive queries, for which millions of rewritings could be generated. We aim at providing an efficient solution to the problem of executing LAV SPARQL query rewritings while the gathered answer is as complete as possible. We formulate the Result-Maximal k-Execution problem (ReMakE) as the problem of maximizing the query results obtained from the execution of only k rewritings. Additionally, a novel query execution strategy called GUN is proposed to solve the ReMakE problem. Our experimental evaluation demonstrates that GUN outperforms traditional techniques in terms of answer completeness and execution time

Simple conceptual graphs revisited: hypergraphs and conjunctive types for efficient projection algorithms

baget2003aInternational audienceSimple Conceptual Graphs (SGs) form the cornerstone for the "Conceptual Graphs" family of languages. In this model, the subsumptio operation is called projection; it is a labelled graphs homomorphism (a NP-hard problem). Designing efficient algorithms to compute projections between two SGs is thus of uttermost importance for the community building languages on top of this basic model. This paper presents some such algorithms, inspired by those developped for Constraint Satisfaction Problems. In order to benefit from the optimization work done in this community, we have chosen to present an alternate version of SGs, differences being the definition of these graphs as hypergraphs and the use of conjunctive types

STYPES: nonrecursive datalog rewriter for linear TGDs and conjunctive queries

We present STYPES, a system that rewrites ontology-mediated queries with linear tuple-generating dependencies and conjunctive queries to equivalent nonrecursive datalog (NDL) queries. The main feature of STYPES is that it produces polynomial-size rewritings whenever the treewidth of the input conjunctive queries and the size of the chases for the ontology atoms as well as their arity are bounded; moreover, the rewritings can be constructed and executed in LOGCFL, indicating high parallelisability in theory. We show experimentally that Apache Flink on a cluster of machines with 20 virtual CPUs is indeed able to parallelise execution of a series of NDL-rewritings constructed by STYPES, with the time decreasing proportionally to the number of CPUs available