Kenneth Baclawski

Quickly generating billion-record synthetic databases

Evaluating database system performance often requires generating synthetic databases—ones having certain statistical properties but filled with dummy information. When evaluating different database designs, it is often necessary to generate several databases and evaluate each design. As database sizes grow to terabytes, generation often takes longer than evaluation. This paper presents several database generation techniques. In particular it discusses: (1) Parallelism to get generation speedup and scaleup. (2) Congruential generators to get dense unique uniform distributions. (3) Special-case discrete logarithms to generate indices concurrent to the base table generation. (4) Modification of (2) to get exponential, normal, and self-similar distributions. The discussion is in terms of generating billion-record SQL databases using C programs running on a shared-nothing computer system consisting of a hundred processors, with a thousand discs. The ideas apply to smaller databases, but large databases present the more difficult problems.

A core ontology for situation awareness

In this paper we present an ontology for situation awareness. One of our goals is to support the claim that this ontology is a reasonable candidate for representing various scenarios of situation awareness. Towards this aim we provide an explanation of the meaning of this ontology, show its expressiveness and demonstrate its extensibility. We also compare the expressiveness of this ontology with alternative approaches we considered during the design of the ontology. We then show how the ontology can be adapted to handle domain-specific situations by readily extending the core language. The extensions include adding subclasses, sub-properties and additional attributes to the core ontology. We conclude with an example of how the ontology can be used to annotate specific instances of a situation.

UML for ontology development

Ontologies are becoming increasingly important because they provide the critical semantic foundation for many rapidly expanding technologies such as software agents, e-commerce and knowledge management (McGuinness, 2002). The Unified Modelling Language (UML)1 has been widely adopted by the software engineering community and its scope is broadening to include more diverse modelling tasks. This paper discusses the recent convergence of UML and ontologies and suggests some possible future directions.

Extending UML to Support Ontology Engineering for the Semantic Web

There is rapidly growing momentum for web enabled agents that reason about and dynamically integrate the appropriate knowledge and services at run-time. The World Wide Web Consortium and the DARPA Agent Markup Language (DAML) program have been actively involved in furthering this trend. The dynamic integration of knowledge and services depends on the existence of explicit declarative semantic models (ontologies). DAML is an emerging language for specifying machine-readable ontologies on the web. DAML was designed to support tractable reasoning.We have been developing tools for developing ontologies in the Unified Modeling Language (UML) and generating DAML. This allows the many mature UML tools, models and expertise to be applied to knowledge representation systems, not only for visualizing complex ontologies but also for managing the ontology development process. Furthermore, UML has many features, such as profiles, global modularity and extension mechanisms that have yet to be considered in DAML.Our paper identifies the similarities and differences (with examples) between UML and DAML. To reconcile these differences, we propose a modest extension to the UML infrastructure for one of the most problematic differences. This is the DAML concept of property which is a first-class modeling element in DAML, while UML associations are not. For example, a DAML property can have more than one domain class. Our proposal is backward-compatible with existing UML models while enhancing its viability for ontology modeling.While we have focused on DAML in our research and development activities, the same issues apply to many of the knowledge representation languages. This is especially the case for semantic network and concept graph approaches to knowledge representations.

Fixed points in partially ordered sets

In this paper we present a number of theorems about fixed points of mappings of partially ordered sets. Our approach is based on a discrete form of the HopfLefschetz fixed point theorem and on order-theoretical analogs of topological constructions. However, we show by example that the fixed point theory of partially ordered sets cannot be reduced to topological fixed point theory. Nevertheless, a substantial number of previously known results in this field are not only subsumed under our approach but are also extended and refined. This is particularly true in the finite case where certain qualitative properties of the fixed point sets come within reach which are stronger than that of merely being nonvoid. We also show that, somewhat surprisingly, fixed point theory has applications to the question of the existence of complements in finite lattices. Let P be a poset (partially ordered set). A self-map is a function f:

SAWA: an assistant for higher-level fusion and situation awareness

Situation awareness involves the identification and monitoring of relationships among level-one objects. This problem in general is intractable (i.e., there is a potentially infinite number of relations that could be tracked) and thus requires additional constraints and guidance defined by the user if there is to be any hope of creating practical situation awareness systems. This paper describes a Situation Awareness Assistant (SAWA) that facilitates the development of user-defined domain knowledge in the form of formal ontologies and rule sets and then permits the application of the domain knowledge to the monitoring of relevant relations as they occur in evolving situations. SAWA includes tools for developing ontologies in OWL and rules in SWRL and provides runtime components for collecting event data, storing and querying the data, monitoring relevant relations and viewing the results through a graphical user interface. An application of SAWA to a scenario from the domain of supply logistics is also presented.

Extending the Unified Modeling Language for ontology development

Abstract.There is rapidly growing momentum for web enabled agents that reason about and dynamically integrate the appropriate knowledge and services at run-time. The dynamic integration of knowledge and services depends on the existence of explicit declarative semantic models (ontologies). We have been building tools for ontology development based on the Unified Modeling Language (UML). This allows the many mature UML tools, models and expertise to be applied to knowledge representation systems, not only for visualizing complex ontologies but also for managing the ontology development process. UML has many features, such as profiles, global modularity and extension mechanisms that are not generally available in most ontology languages. However, ontology languages have some features that UML does not support. Our paper identifies the similarities and differences (with examples) between UML and the ontology languages RDF and DAML+OIL. To reconcile these differences, we propose a modification to the UML metamodel to address some of the most problematic differences. One of these is the ontological concept variously called a property, relation or predicate. This notion corresponds to the UML concepts of association and attribute. In ontology languages properties are first-class modeling elements, but UML associations and attributes are not first-class. Our proposal is backward-compatible with existing UML models while enhancing its viability for ontology modeling. While we have focused on RDF and DAML+OIL in our research and development activities, the same issues apply to many of the knowledge representation languages. This is especially the case for semantic network and concept graph approaches to knowledge representations.

Cohen-Macaulay ordered sets

The purpose of this paper is to introduce a new kind of partially ordered set: the Cohen-Macaulay poset. It is now known that this concept provides some interesting connections among Algebraic Topology, Combinatorics, Commutative Algebra and Homological Algebra, and numerous individuals have contributed to the theory. Some of these are Stanley [35, 36, 371, Reisner [26], Hochster [21] and Garsia [17]. The notion of a Cohen-Macaulay poset originated in the author’s thesis [2], and many of the results of this paper are also there in some form. The original motivation for introducing this concept was to provide a reasonable setting for the results of [I] and to find techniques for proving unimodality theorems. The Rank Selection Theorem (5.4) h a d much to do with this. At the time we referred to these posets as Folkman posets because of Folkman’s work in [16]. The term “Cohen-Macaulay” was later suggested by Kempf, who pointed out the relationship with the theory of Local Cohomology as, for example, in [22]. The basic tool for proving our results is the theory of homology of diagrams on posets. Diagrams, even without homology, are related to certain purely combinatorial constructions. For an example of this see [4]. By using diagrams in more sophisticated ways one can prove some quite interesting combinatorial theorems, as was done for example in [6] using results from [3]. Although we have consistently used poset homology to prove the results in this paper, one could also prove them using ring theory methods. In a joint paper with Garsia [7], the latter approach is employed. The fact that one can define Cohen-Macaulay posets using either homology theory or ring theory is a consequence of a remarkable theorem of Reisner [26]. An “elementary” proof of this important theorem appears in [7]. One of the most dramatic applications of Cohen-Macaulay posets (or more precisely of Cohen-Macaulay complexes) is the proof by Stanley [35] of the

Whitney numbers of geometric lattices

Publisher Summary This chapter discusses Whitney numbers of geometric lattices. There is a homology theory on the category of ordered sets such that the Betti numbers of a geometric lattice are the Whitney numbers of the first kind. The chapter describes such a theory. The theory is a sheaf cohomology on a topological space associated to the ordered set. It is, however, also possible to develop the theory in terms of specific simplicial chain complexes.

Derivation of ontological relations using formal methods in a situation awareness scenario

This paper describes a case study of relation derivation within the context of situation awareness. First we present a scenario in which inputs are supplied by a simulated Level 1 system. The inputs are events annotated with terms from an ontology for situation awareness. This ontology contains concepts used to represent and reason about situations. The ontology and the annotations of events are represented in DAML and Rule-ML and then systematically translated to a formal method language called MetaSlang. Having all information expressed in a formal method language allows us to use a theorem prover, SNARK, to prove that a given relationship among the Level 1 objects holds (or that it does not hold). The paper shows a proof of concept that relation derivation in situation awareness can be done within a formal framework. It also identifies bottlenecks associated with this approach, such as the issue of the large number of potential relations that may have to be considered by the theorem prover. The paper discusses ways of resolving this as well as other problems identified in this study.