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## Publications

Publications (113)

Nesting is a fundamental and very commonly used programming construct. In many cases, the wise use of nesting contributes significantly to a programming team elegantly designing a solution to a difficult problem. However, the ease with which nesting constructs may be created and the essentially unlimited depth and breadth to which they may exist al...

The importance of prerequisites for education has recently become a promising research direction. This work proposes a statistical model for measuring dependencies in learning resources between knowledge units. Instructors are expected to present knowledge units in a semantically well-organized manner to facilitate students’ understanding of the ma...

The main challenge that can impact the effectiveness of authentication mechanisms is human error (unintentional threats). Irrational judgment associated with human error is often linked to a unique attribute called cognitive bias (CB). CB is a tendency to think irrationally in certain situations and make irrational judgment. The appearance of CB in...

The Vector Space Model (VSM), is the main technique to model the semantics from the text. However, the VSM model suffers from notable limitations. The main alternative model for VSM model is a graph-based model. This paper presents a systematic review on the graph-based processes of Semantic Learning, Representing and Growth (SLRG) from the text. T...

Recently, J.~T.~Denniston, A.~Melton, and S.~E.~Rodabaugh introduced a lattice-valued analogue of the concept of institution of J.~A.~Goguen and R.~M.~Burstall, comparing it, moreover, with the (lattice-valued version of the) notion of topological system of S.~Vickers. In this paper, we show that a suitable generalization of topological systems pro...

Motivated by the concept of Sierpinski object for topological systems of S.~Vickers, presented recently by R.~Noor and A.~K.~Srivastava, this paper introduces the Sierpinski object for many-valued topological systems and shows that it has three important properties of the crisp Sierpinski space of general topology.

Security models have been designed to ensure data is accessed and used in proper manner according to the security policies. Unfortunately, human role in designing security models has been ignored. Human behavior relates to many security breaches and plays a significant part in many security situations.In this paper, we study users' security decisio...

Semantic-based text document clustering aims to group documents into a set of topic clusters. We propose a new approach for semantically clustering of text documents based on cognitive science and graph theory. We apply a computational cognitive model of semantic association for human semantic memory, known as Incremental Construction of an Associa...

Motivated by the concept of Sierpinski object for topological systems of S. Vickers, presented recently by R. Noor and A.K. Srivastava, this paper introduces the Sierpinski object for many-valued topological systems and shows that it has three important properties of the crisp Sierpinski space of general topology.

Concepts in web ontologies help machines to understand data through the meanings they hold. Furthermore, learning contexts and topics of web documents also have helped in better semantic-oriented structuring and retrieval of data on the web. In this short paper we present a novel approach for domain-independent open learning of domain concepts, con...

Concepts in web ontologies help machines to un- derstand data through the meanings they hold. Furthermore, learning contexts and topics of web documents also have helped in better semantic-oriented structuring and retrieval of data on the web. In this short paper we present a novel approach for domain-independent open learning of domain concepts, c...

The Semantic Web vision provides the current Web with the necessary infrastructure that allows the computer to process knowledge. One of the cornerstones of this infrastructure is the Ontology. Ontology is a formal way of sharing knowledge via a machine-readable format in order to facilitate the reuse of the knowledge among different parties. For e...

We present an extension using RBAC to our published dynamic integrity model. In our published work we presented a dynamic integrity model based on a metric we call the modification factor to evaluate whether the integrity level should be changed up or down dynamically. The RBAC extension we propose in this paper is to address certain situations whi...

Proper access control is one of the most important issues in computer security. It consists of securing a system with respect to availability, confidentiality, and integrity. Integrity is about making sure that only proper modifications take place. Some integrity models are static in nature, which may limit their capabilities for better protection...

Object-oriented systems are dynamic and have to be constantly maintained, or they become aged and irrelevant. Many costly software issues exist due to poorly designed systems and due to systems which are not easy to test or maintain because of poor designs. Martin's metrics [1] are well-known package design metrics that can be used in early stages...

Recently, J.T. Denniston, A. Melton, and S.E. Rodabaugh introduced a lattice-valued analogue of the concept of institution of J.A. Goguen and R.M. Burstall, comparing it, moreover, with the (lattice-valued version of the) notion of topological system of S. Vickers. In this paper, we show that a suitable generalization of topological systems provide...

Object-oriented systems are dynamic and have to be constantly maintained, or they become aged and irrelevant. Poor choices made during design phase result in costly problems. Hence, design metrics should be an essential part of the agile software development process. Martin's metrics [1] are wellknown package design metrics that can be used in earl...

Many costly software issues exist due to poorly designed systems and due to systems which are not easy to test or maintain because of poor designs. R. C. Martin began with a set of object oriented design principles and designed his metrics based on these principles. In a previous paper [2], we began with Martin's principles and used them to modify...

With the increasing number of Web services, the Semantic Web research community is moving toward enhancing procedures so that clients may effectively discover appropriate Web services that maximally satisfy not only functional but also non-functional requirements. Using purely syntactic approaches to discover Web services has limited efficiency. Th...

RDF data is growing exponentially and expanding rapidly from different sources everyday. Storing large-scale RDF data has been a matter of concern since the beginning of the Semantic Web. In the recent past, multiple approaches for storing RDF data have been suggested, ranging from simple storages to advanced methods like clustering predicates, whi...

The World Wide Web is considered one of the main sources in accessing information. Over the last decades, a number of improvements have been achieved that helped the Web reach its current state. For many, the World Wide Web has become indispensable to their daily lives. There are a number of research projects going on to enhance the current status...

A question from programming arises: if bitstring x compares with bitstring y to some degree , and if bitstring y satisfies predicate a to some degree , then how should the possibility be mathematically modeled that bitstring x satisfies predicate a to at least some degree related to both and ? Mathematically modeling this question is surprisingly i...

R. C. Martin and others have defined package cohesion metrics. Martin has also developed package cohesion principles that can help developers' partition classes into packages. Careful analysis of these cohesion principles indicates that cohesion is multifaceted. Based on these principles, in this paper we introduce two types or aspects of package c...

Over the last few decades, a lot of research has been done to measure software quality including using high-level design metrics to measure the quality of the design. R. C. Martin's metrics are some of the best-known software package metrics. Martin began with a set of object oriented design principles and designed his metrics based on these princi...

RDF data is growing exponentially and expanding rapidly from different sources everyday. Storing large-scale RDF data has been a matter of concern since the beginning of the Semantic Web. In the recent past, multiple approaches for storing RDF data have been suggested, ranging from simple storages to advanced methods like clustering predicates, whi...

Nesting is a fundamental and very commonly used programming construct. In many cases, the wise use of nesting contributes significantly to a programming team's elegantly designing a solution to a difficult problem. However, the ease with which nesting constructs may be created and the essentially unlimited depth and breadth to which they may exist...

The Semantic Web is a collection of components that work together so that a machine is able to process and understand information. In order for this vision to be fully realized, formal standards for representing and interpreting data must be determined and enforced. These formal standards include the Resource Description Framework (RDF) and machine...

This paper provides variable-basis lattice-valued analogues of the well-known results that the construct Prost of preordered sets, firstly, is concretely isomorphic to a full concretely coreflective subcategory of the category Top of topological spaces (which employs the concept of the dual of the specialization preorder), and, secondly, is (non-co...

This paper examines the synergism emerging from three historically distinctive traditions: theory of locales; programming semantics and topological systems; and point-set lattice-theoretic (poslat) topology, both fixed-basis and variable-basis. Many gaps are discovered and filled with new results; and open questions are posed.

Formal concept analysis (FCA) is built on a special type of Galois
connections called polarities. We present new results in formal concept
analysis and in Galois connections by presenting new Galois connection results
and then applying these to formal concept analysis. We also approach FCA from
the perspective of collections of formal contexts. Usu...

This paper links formal concept analysis (FCA) both to order-theoretic developments in the theory of Galois connections and to Chu spaces or systems viewed as a common rubric for both topological systems and systems arising from predicate transformers in programming semantics [13]. These links are constructed for each of traditional FCA and LL-FCA,...

As software systems become more complex and difficult to maintain, data mining techniques become more important to software engineering. Increased software engineering data motivates the use of data mining techniques. Data mining in software engineering can play crucial roles in software quality and productivity. Frequent pattern mining is one of t...

Though software measurement is relatively new -seriously beginning in the 1970s, measurement is well developed in many disciplines, and measurement theory is itself a well developed discipline. Probably because software engineering has developed so very quickly and because managers understand the value of measurement, the field of software measurem...

This paper is primarily dedicated to understanding the natural role that topological systems and lattice-valued topological systems play in understanding the relationship between algebra and topology, a relationship expressed by an “interweaving” of embeddings of (essentially) algebraic and topological categories. This natural role is revealed by h...

We are developing a general education mathematics course that will introduce students to mathematical reasoning and applications. The course will cover the history of, the motivation for, and an introduction to cryptography, fuzzy set theory, graph theory, and non-Euclidean geometry. Three weeks (nine discussion-lecture hours) will be devoted to ea...

Usually, when Galois connections are generalized categorically, they are generalized to adjoint situations. Unfortunately, in this generalization many interesting properties are lost. Recently, Galois connections have been generalized in a concrete category setting to form Galois correspondences. Fortunately, this generalization preserves many Galo...

Numerous research results in the areas of software measures and software tools are predicated on a particular programming language, or on some characterizations of a programming language. For example, numerous software measures have been defined only for structured programming languages and several of the reported approaches to program testing defi...

Galois connections - also called residuated/residual maps - have been studied and used extensively in both mathematics and computer science. In the 1980s, Galois connections were generalized to connections, and in the 1990s, a counterpart to Galois connections, called Lagois connections, were discovered. Lagois connections, as the name suggests, ar...

"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied inter...

: We provide the rudiments of the theory of Galois connections (or residuation theory, as it is sometimes called) together with many examples and applications. Galois connections occur in profusion and are well-known to most mathematicians who deal with order theory; they seem to be less known to topologists. However, because of their ubiquity and...

Foreword and DedicationThis volume contains the Proceedings of the Eleventh Conference on the Mathematical Foundations of Programming Semantics. The Conference was held on the campus of Tulane University, New Orleans, LA from March 29 to April 1, 1995.The papers in this volume were reviewed or were solicited by the Organizers and Program Committee...

In this paper we define a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the definition of Galois connection and some of its properties; next we define Lagois connection, establish some of its properties, and compare these with propertie...

Hagino (1987) develops CPL, a categorical programming language based on dialgebras which include algebras, coalgebras, products, sums and exponentials. We give an introduction to dialgebras and CPL.Working from the well-known correspondence between cartesian closed categories (CCCs) and λ-calculi (Lambek, 1980; Curien, 1986), we study the relations...

The major goal of this conference series is to bring together computer scientists who work in programming semantics and mathematicians who work in areas which might impact programming semantics so that they may share ideas and discuss problems of mutual interest. By letting mathematicians see applications of their work to programming semantics and...

The extention principle of fuzzy set theory provides a method to extend an operation on elements of a set Y to a power operation on fuzzy subsets of Y. We generalize this idea to obtain for any fuzzy relation π over Y, a fuzzy power relation π+ over the fuzzy power set of Y. If ϱ is a metric, ϱ+ generalizes the Hausdorff metric on the crisp power s...

The fuzzy relational database model as defined by Buckles and Petry employs sets in place of atomic values for components of tuples in database relations. This technique for dealing with imprecision in relational databases is intuitively appealing. Moreover, the model preserves several important properties of classical relational databases. In rece...

Software metrics' research has produced as many failures as successes. Theoretical results supported by application experiences help us understand many of the pitfalls. We will discuss how some of these pitfalls can be avoided and how metrics' research can be made more robust so that we can improve the measurements.

This volume contains the proceedings of the Seventh International Conferenceon the Mathematical Foundations of Programming Semantics, held at Carnegie Mellon University, March 1991. The conference continued a series of annual meetings, alternating between workshop and conference formats, intended to bring together computer scientists and mathematic...

This paper deals with the connections existing between fuzzy set theory and fuzzy relational databases. Our new result dealing with fuzzy relations is how to calculate the greatest lower bound (glb) of two similarity relations. Our main contributions in fuzzy relational databases are establishing from fuzzy set theory what a fuzzy relational databa...

It is well-known that Galois connections are useful in describing some situations that occur naturally in computer science and mathematics; and recently it has been shown that Lagois connections, which are closely related to Galois connections, are similarly useful. Thus, it is natural to ask if there are not common generalizations of Galois and La...

We, the Grubstake Group, are committed to creating an environment in which software metrics can be used confidently, effectively, and in full knowledge of their limitations. We responded to a lack of rigor in software measurement, and concentrated our efforts towards the development of a suitable theory and foundation. We explained our concerns and...

We investigate three types of software metrics which we call internal, external, and predictive software metrics. These three types of software metrics allow for a complete classification of all software metrics. In this paper, however, our main purpose is not to classify metrics; our main purpose is to explain what the specification of a metric sh...

An abstract is not available.

The technique of employing sets of values for tuple components to express imprecision in relational databases was proposed by Buckles and Petry in their classic works on fuzzy relational databases. In addition to providing an intuitively appealing scheme for representing fuzzy information, the model of Buckles and Petry possesses several key proper...

The fuzzy relational database model proposed by Buckles and Petry is a formal method for organizing and using fuzzy information in relational databases. The model possesses two key properties that hold for classical relational databases: no two tuples have identical interpretations and each relational algebra operation has a unique result. The orig...

Basic principles which necessarily underlie software measures
research are analysed. In the prevailing paradigm for the validation of
software measures, there is a fundamental assumption that the sets of
measured documents are ordered and that measures should report these
orders. The authors describe mathematically, the nature of such orders.
Consi...

Many software engineering methods place internal structural constraints on the documents (including specifications, designs, and code) that are produced. Examples of such structural constraints are low coupling, high cohesion, reuse in designs and code, and control structuredness and data-abstraction in code. The use of these methods is supposed to...

We as a group—called the Grubstake Group—are convinced that software measures are essential for “controlling” software. Thus, we are dedicated to producing an environment in which software measures can be confidently used by software managers and programmers. However, we are also convinced that such an environment can only be created if there exist...

The fuzzy relational model of Buckles and Petry is a rigorous scheme for incorporating non-ideal or fuzzy information in a relational database. In addition to providing a consistent scheme for representing fuzzy information in the relational structure, the model possesses two critical properties that hold for classical relational databases. These p...

The authors define a software process model (SPM). The SPM is a
model of evolution of the full set of documents produced in a software
project. It is a general model for software development using any
development approach, providing a framework for measuring, analyzing,
and understanding the software development process. The authors use the
model t...

A solution is obtained to the problem of defining a software
measure or a family of measures which simultaneously detect those
aspects of software complexity that are detected by the software science
measures and the cyclomatic number. The authors present a family of
measures, called weighted measures that is built on the software science
measures...

Software measures and software tools are often defined in terms of a particular, limited programming language. For example, a number of software measures are defined only for structured programs. Several approaches to program testing and debugging are defined using a specific simple language. As a result, implementing tools and measures so that the...

Informally we show why a domain with a reasonable collection of properties is a topological space. We then address the question: if one wishes to do programming language semantics in a category of topological spaces instead of the category of complete partial orders (cpos) which category should be used? This question is first considered with respec...

This volume is the proceedings of the 3rd Workshop on the Mathematical Foundations of Programming Language Semantics held at Tulane University, New Orleans, Louisiana, April 8-10, 1987. The 1st Workshop was at Kansas State University, Manhattan, Kansas in April, 1985 (see LNCS 239), and the 2nd Workshop with a limited number of participants was at...

We study Galois connections by examining the properties of three categories. The objects in each category are Galois connections. The categories differ in their hom-sets; in the most general category the morphisms are pairs of functions which commute with the maps of the domain and codomain Galois connections. One of our main results is that one of...