Manolis Koubarakis

Composing cardinal direction relations

We study the recent proposal of Goyal and Egenhofer who presented a model for qualitative spatial reasoning about cardinal directions. Our approach is formal and complements the presentation of Goyal and Egerdaofer. We focus our efforts on the composition operator for two cardinal direction relations. We consider two interpretations of the composition operator: consistency-based and existential composition. We point out that the only published method to compute the consistency-based composition does not always work correctly. Then, we consider progressively more expressive classes of cardinal direction relations and give consistency-based composition algorithms for these classes. Our theoretical framework allows us to prove formally that our algorithms are correct. When we consider existential composition, we demonstrate that the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by Goyal and Egenhofer. Finally, we discuss some extensions to the basic model and consider the composition problem for these extensions.

A formal framework for business process modelling and design

We present a formal framework for enterprise and business process modelling. The concepts of our framework (objectives and goals, roles and actors, actions and processes, responsibilities and constraints) allow business analysts to capture enterprise knowledge in a way that is both intuitive and mathematically formal. We also outline the basic steps of a methodology that allows business analysts to produce detailed, formal specifications of business processes from high-level enterprise objectives. The use of a formal language permits us to verify that the specifications possess certain correctness properties, namely that the responsibilities assigned to roles are fulfilled, and that constraints are maintained as a result of process execution.

Modeling and querying metadata in the semantic sensor web: the model stRDF and the query language stSPARQL

RDF will often be the metadata model of choice in the Semantic Sensor Web. However, RDF can only represent thematic metadata and needs to be extended if we want to model spatial and temporal information. For this purpose, we develop the data model stRDF and the query language stSPARQL. stRDF is a constraint data model that extends RDF with the ability to represent spatial and temporal data. stSPARQL extends SPARQL for querying stRDF data. In our extension to RDF, we follow the main ideas of constraint databases and represent spatial and temporal objects as quantifier-free formulas in a first-order logic of linear constraints. Thus an important contribution of stRDF is to bring to the RDF world the benefits of constraint databases and constraint-based reasoning so that spatial and temporal data can be represented in RDF using constraints.

Strabon: a semantic geospatial DBMS

We present Strabon, a new RDF store that supports the state of the art semantic geospatial query languages stSPARQL and GeoSPARQL. To illustrate the expressive power offered by these query languages and their implementation in Strabon, we concentrate on the new version of the data model stRDF and the query language stSPARQL that we have developed ourselves. Like GeoSPARQL, these new versions use OGC standards to represent geometries where the original versions used linear constraints. We study the performance of Strabon experimentally and show that it scales to very large data volumes and performs, most of the times, better than all other geospatial RDF stores it has been compared with.

Database models for infinite and indefinite temporal information

Abstract Representation and querying of temporal information can benefit from the integration of techniques from constraint databases, database models for indefinite information and reasoning about temporal constraints. With this perspective in mind, we present a hierarchy of temporal data models: temporal relations, generalized temporal relations and temporal tables. We study the semantics of these models and develop algebraic and calculus query languages for them. The proposed models can be useful to several novel applications include planning, scheduling, project management, medical information systems, geographical information systems and natural language processing systems.

Publish/Subscribe for RDF-based P2P Networks

Publish/subscribe systems are an alternative to query based systems in cases where the same information is asked for over and over, and where clients want to get updated answers for the same query over a period of time. Recent publish/subscribe systems such as P2P-DIET have introduced this paradigm in the P2P context. In this paper we built on the experience gained with P2P-DIET and the Edutella P2P infrastructure and present the first implementation of a P2P publish/subscribe system supporting metadata and a query language based on RDF. We define formally the basic concepts of our system and present detailed protocols for its operation. Our work utilizes the latest ideas in query processing for RDF data, P2P indexing and routing research.

RDFS Reasoning and Query Answering on Top of DHTs

We study the problem of distributed RDFS reasoning and query answering on top of distributed hash tables. Scalable, distributed RDFS reasoning is an essential functionality for providing the scalability and performance that large-scale Semantic Web applications require. Our goal in this paper is to compare and evaluate two well-known approaches to RDFS reasoning, namely backward and forward chaining, on top of distributed hash tables. We show how to implement both algorithms on top of the distributed hash table Bamboo and prove their correctness. We also study the time-space trade-off exhibited by the algorithms analytically, and experimentally by evaluating our algorithms on PlanetLab.

On the consistency of cardinal direction constraints

We present a formal model for qualitative spatial reasoning with cardinal directions utilizing a co-ordinate system. Then, we study the problem of checking the consistency of a set of cardinal direction constraints. We introduce the first algorithm for this problem, prove its correctness and analyze its computational complexity. Utilizing the above algorithm, we prove that the consistency checking of a set of basic (i.e., non-disjunctive) cardinal direction constraints can be performed in O(n^5) time. We also show that the consistency checking of a set of unrestricted (i.e., disjunctive and non-disjunctive) cardinal direction constraints is NP-complete. Finally, we briefly discuss an extension to the basic model and outline an algorithm for the consistency checking problem of this extension.

Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning

We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fouriers algorithm for linear inequalities. Finally, we use these results to provide new temporal reasoning algorithms for the Ord-Horn subclass of Allens interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the Ord-Horn subclass. This property distinguishes the Ord-Horn subclass from the pointizable subclass (for which strong 5-consistency is sufficient to guarantee global consistency), and the continuous endpoint subclass (for which strong 3-consistency is sufficient to guarantee global consistency). Copyright 2001. Elsevier Science B.V.

Tractable disjunctions of linear constraints

We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and inequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fouriers algorithm for linear inequalities.