In this paper we deal with an original model of technically oriented cognitive semantics of modal equivalences, stated in semi-controlled natural languages and used as surface linguistic representations of internal knowledge states of artificial autonomous systems. The cognitive semantics is defined to support generation of natural language statements extended with auto-epistemic operators of modality, representing subjectively experienced certainty, strong belief and week belief of the autonomous system that the relationship between occurrence of two chosen properties in a real object is the logical equivalence relation. An internal architecture of the autonomous system is briefly presented with particular emphasis on computational modules responsible for verification of compliance of current knowledge processing states with states described by the cognitive semantics as proper for application of a particular case of modal equivalence. The major issue discussed in the paper concerns an original theory of grounding of modal equivalences in empirical knowledge resources, encapsulated in the autonomous system. The whole theory consists of theorems describing basic and advanced properties of the cognitive semantics. In the paper, the attention is limited to presentation and proof of four theorems about nonemptiness of the proposed cognitive semantics. The research results cover the next stage of some research and development efforts, concerning the technical implementation of cognitive computing models, describing the artificial generation of semi-natural languages by the interactive autonomous system to describe their encapsulated knowledge resources.
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Cognitive Informatics is a cutting-edge and multidisciplinary research area that tackles the fundamental problems shared by modern informatics, computing, software engineering, AI, cybernetics, cognitive science, neuropsychology, medical science, systems science, philosophy, linguistics, economics, management science, and life sciences. This editorial introduces the emerging field of cognitive informatics and its applications in cognitive computing, abstract intelligence, computational mathematics, and computational intelligence. The themes and structure of this special issue on cognitive informatics are described, and then, focuses of the selected papers in this special issue are highlighted.
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Cognitive Informatics is a cutting-edge and multidisciplinary research area that tackles the fundamental problems shared by modern informatics, computing, software engineering, AI, cybernetics, cognitive science, neuropsychology, medical science, systems science, philosophy, linguistics, economics, management science, and life sciences. This editorial introduces the emerging field of cognitive informatics and its applications in cognitive computing, abstract intelligence, computational mathematics, and computational intelligence. The themes and structure of this special issue on cognitive informatics are described, and then, focuses of the selected papers in Part II of this special issue are highlighted.
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The abstract, rigorous, and expressive needs in cognitive informatics, intelligence science, software science, and knowledge science lead to new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of expressive mathematical structures that deals with high level mathematical entities beyond numbers and sets, such as abstract objects, complex relations, behavioral information, concepts, knowledge, processes, and systems. Denotational mathematics is usually in the form of abstract algebra that is a branch of mathematics in which a system of abstract notations is adopted to denote relations of abstract mathematical entities and their algebraic operations based on given axioms and laws. Four paradigms of denotational mathematics, known as concept algebra, system algebra, Real-Time Process Algebra (RTPA), and Visual Semantic Algebra (VSA), are introduced in this paper. Applications of denotational mathematics in cognitive informatics and computational intelligence are elaborated. Denotational mathematics is widely applicable to model and manipulate complex architectures and behaviors of both humans and intelligent systems, as well as long chains of inference processes.
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Cognitive informatics (CI) is the transdisciplinary enquiry of cognitive and information sciences that investigates into the internal information processing mechanisms and processes of the brain and natural intelligence, and their engineering applications via an interdisciplinary approach. CI develops a coherent set of fundamental theories and denotational mathematics, which form the foundation for most information and knowledge based science and engineering disciplines such as computer science, cognitive science, neuropsychology, systems science, cybernetics, software engineering, knowledge engineering, and computational intelligence. This paper reviews the central doctrine of CI and its applications. The theoretical framework of CI is described on the architecture of CI and its denotational mathematic means. A set of theories and formal models of CI is presented in order to explore the natural and computational intelligence. A wide range of applications of CI are described in the areas of cognitive computers, cognitive properties of knowledge, simulations of human cognitive behaviors, cognitive complexity of software, autonomous agent systems, and computational intelligence.
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