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Cognitive informatics studies the natural intelligence and the brain from a theoretical and a computational approach, which rigorously explains the mechanisms of the brain by a fundamental theory known as abstract intelligence, and formally models the brain by contemporary denotational mathematics. This paper, as an extended summary of the invited keynote presented in AMT-BI 2010, describes the interplay of cognitive informatics, abstract intelligence, denotational mathematics, brain informatics, and computational intelligence. Some of the theoretical foundations for brain informatics developed in cognitive informatics are elaborated. A key notion recognized in recent studies in cognitive informatics is that the root and profound objective in natural, abstract, and artificial intelligence in general, and in cognitive informatics and brain informatics in particular, is to seek suitable mathematical means for their special needs that were missing in the last six decades. A layered reference model of the brain and a set of cognitive processes of the mind are systematically developed towards the exploration of the theoretical framework of brain informatics. The current methodologies for brain studies are reviewed and their strengths and weaknesses are analyzed. A wide range of applications of cognitive informatics and denotational mathematics are recognized in brain informatics toward the implementation of highly intelligent systems such as world-wide wisdom (WWW+), cognitive knowledge search engines, autonomous learning machines, and cognitive robots.

Concept algebra is an abstract mathematical structure for the formal treatment of concepts and their algebraic relations, operations, and associative rules for composing complex concepts, which provides a denotational mathematic means for knowledge system representation and manipulation. This paper presents an implementation of concept algebra by a set of simulations in Java. A visualized knowledge representation tool for concept algebra is developed, which enables machines learn concepts and knowledge autonomously. A set of eight relational operations and nine compositional operations of concept algebra are implemented in the tool to rigorously manipulate knowledge by concept networks. The knowledge representation tool is capable of presenting concepts and knowledge systems in multiple ways in order to simulate and visualize the dynamic concept networks during machine learning based on concept algebra.

Memorization is a key cognitive process of the brain because almost all human intelligence is functioning based on it. This paper presents a neuroinformatics theory of memory and a cognitive process of memorization. Cognitive informatics foundations and functional models of memory and memorization are explored toward a rigorous explanation of memorization. The cognitive process of memorization is studied that reveals how and when memory is created in long-term memory. On the basis of the formal memory and memorization models, the cognitive process of memorization is rigorously described using Real-Time Process Algebra (RTPA). This work is one of the fundamental enquiries on the mechanisms of the brain and natural intelligence according to the Layered Reference Model of the Brain (LRMB) developed in cognitive informatics.

Denotational mathematics is a category of expressive mathematicalstructures that deals with high-level mathematical entities beyond numbers andsets, such as abstract objects, complex relations, behavioral information, concepts,knowledge, processes, intelligence, and systems. New forms of mathematicsare sought, collectively known as denotational mathematics, in order todeal with complex mathematical entities emerged in cognitive informatics,computational intelligence, software engineering, and knowledge engineering.The domain and architecture of denotational mathematics are presented in thispaper. Three paradigms of denotational mathematics, known as concept algebra,system algebra, and Real-Time Process Algebra (RTPA), are introduced.Applications of denotational mathematics in cognitive informatics and computationalintelligence are elaborated. A set of case studies is presented on themodeling of iterative and recursive systems architectures and behaviors byRTPA, the modeling of autonomic machine learning by concept algebra, andthe modeling of granular computing by system algebra.

Games are a complex mathematical structure for modeling dynamicdecision processes under competition where opponent players compete for themaximum gain or toward a success state in the same environment according tothe same rules of the game. Games are conventionally dealt with payoff tablesbased on random strategies, which are found inadequate to describe the dynamicbehaviors of games and to rigorously predict the outcomes of games.This paper presents an abstract game theory, which enables a formal treatmentof games by a set of mathematical models for both the layouts and behaviors ofgames. A generic mathematical model of abstract games is introduced, based onwhich the properties of games in terms of decision strategies and serial matchesare described. A wide range of generic zero-sum and nonzero-sum games areformally modeled and analyzed using the generic mathematical models of abstractgames.

Recent studies on the laws and mathematical constraints of softwarehave resulted in fundamental discoveries in computing and software engineeringtoward exploring the nature of software. It was recognized that software isnot constrained by any physical laws discovered in the natural world. However,software obeys the laws of mathematics, cognitive informatics, system science,and formal linguistics. This paper investigates into the mathematical laws ofsoftware and computing behaviors. A generic mathematical model of programsis created that reveals the nature of software as abstract processes and itsuniqueness beyond other mathematical entities such as sets, relations, functions,and abstract concepts. A comprehensive set of mathematical laws for softwareand its behaviors is established based on the generic mathematical model ofprograms and the fundamental computing behaviors elicited in Real-Time ProcessAlgebra (RTPA). A set of 95 algebraic laws of software behaviors is systematicallyderived, which encompasses the laws of meta-processes, processrelations, and system compositions. The comprehensive set of mathematicallaws of software lays a theoretical foundation for analyzing and modeling softwarebehaviors and software system architectures, as well as for guiding rigorouspractice in programming. They are also widely applicable for the rigorousmodeling and manipulation of human cognitive processes and computational intelligentbehaviors.

The denotational and expressive needs in cognitive informatics,computational intelligence, software engineering, and knowledge engineeringlead to the development of new forms of mathematics collectively known asdenotational mathematics. Denotational mathematics is a category ofmathematical structures that formalize rigorous expressions and long-chain inferences of system compositions and behaviors with abstract concepts,complex relations, and dynamic processes. Typical paradigms of denotationalmathematics are such as concept algebra, system algebra, Real-Time ProcessAlgebra (RTPA), Visual Semantic Algebra (VSA), fuzzy logic, and rough sets.A wide range of applications of denotational mathematics have been identifiedin many modern science and engineering disciplines that deal with complex andintricate mathematical entities and structures beyond numbers, Booleanvariables, and traditional sets.

Although there are various ways to express entities, notions, relations, actions, and behaviors in natural languages, it is found in Cognitive Informatics (CI) that human and system behaviors may be classified into three basic categories known as to be, to have, and to do. All mathematical means and forms, in general, are an abstract and formal description of these three categories of system behaviors and their common rules. Taking this view, mathematical logic may be perceived as the abstract means for describing ‘to be,' set theory for describing ‘to have,' and algebras, particularly the process algebra, for describing ‘to do.' This paper presents the latest development in a new transdisciplinary field known as CI. Three types of new mathematical structures, Concept Algebra (CA), System Algebra (SA), and Real-Time Process Algebra (RTPA), are created to enable rigorous treatment of knowledge representation and manipulation in terms of to be / to have / to do in a formal and coherent framework. A wide range of applications of the three knowledge algebras in the framework of CI has been identified in knowledge and software engineering

It is recognized that human and system behaviors may be modeled by a 3-D process comprising actions, time, and space. Software behaviors, similarly, can be modeled in the three dimensions known as the mathematical operations, event/process timing, and memory manipulation. This paper introduces Real- Time Process Algebra (RTPA) as a coherent software engineering notation system. RTPA is used to address the 3-D problem in software system description and specification in terms of architecture, static and dynamic behaviors. Case studies on applications of RTPA in real-time system modeling and specification are provided in this paper with real-world examples.

This paper presents a European approach to the development of a new industrial architecture of commercial off-the-shelf (COTS) software components, and a practical technology for design and implementation of test-reusable COTS. This work, known as the European COMPONENT+ project, is supported by the European 5th Framework programme and by a number of leading industrial partners in componentbased software engineering.Existing COTS architectural technologies were focused on code reuse. The following fundamental problems inherited in conventional COTS technologies have been identified: a) Low testability for end-users; b) Low maintainability for end-users; c) No support for run-time testing; and d) Separated software code and test cases.Being oriented to the problems and challenges as identified above, this paper presents new solutions and techniques for testable COTS architecture developed in the European Component+ project, such as: a) A new technology for implementing BIT-based COTS; b) A new approach to COTS test; c) An extension of OO technology from code reuse to test reuse in COTS development; and d) A new approach to enabling COTS test at run-time. BIT components can be embedded in any conventional COTS for enabling test reuse as well as code reuse. The BIT + COST technologies have been found a wide range of applications in component-based software engineering.

Cognitive informatics (CI) is a cutting-edge and profound interdisciplinary research area that tackles the common root problems and foundations of modern informatics, computation, software engineering, AI, and life sciences. CI is a new frontier that studies internal information processing mechanisms and processes of the brain, and their applications in computing, software, and ICT industries. Conventional information theory (Shannon, 1948) treated information as a measure of the probability of messages received from a channel. It was focused on information transmission rather than information itself. Modern information theory perceives information as any aspect of the natural world that can be abstracted and digitally represented. With this orientation, information is regarded as entities of messages, rather than a probabilistic measurement of them as in the classical information theory. However, it is recognized that current information theories are still in a category of external informatics. Complementing to these, there is a whole range of extremely interesting new research areas known as CI, a term which was coined by the author in 2001. I think, therefore I am (Rene Descartes, 1596–1650).’ CI draws the attention of research on the internal information processing mechanisms of the brain, which are perceived as the foundation of next generation IT and software technologies, such as neural computers, bio-computers, novel methodologies of software engineering, quantum information processing, and powerful ICT systems. This talk focuses on the natural information processing mechanisms and cognitive processes. The latest development on CI at the First IEEE International Conference on Cognitive Informatics (ICCI’02) will be reported. At heoretical framework of CI as an emerging and interdisciplinary research area will be presented. The objectives of this talk are to draw attention of researchers, practitioners and graduate students on the investigation of cognitive mechanisms and processes of human information processing, and to stimulate the collaborative international effort on CI research and engineering applications.

This paper proposes a Software Engineering Process (SEP) benchmarking methodology and a benchmark-gap analysis technique to assist industrial practitioners in quantitative software engineering. This work adopts the comprehensive SEP Assessment model (SEPRM), as a foundation to SEP benchmarking. In this approach, a number of conventional benchmarking challenges may be overcome. Case studies are presented to demonstrate the usage of the benchmarking technologies and supporting tools.