On the Mathematical Theories and Cognitive Foundations of Information

On the Mathematical Theories and Cognitive Foundations of Information

Yingxu Wang (University of Calgary, Canada)
DOI: 10.4018/978-1-5225-1759-7.ch005
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Abstract

A recent discovery in computer and software sciences is that information in general is a deterministic abstract quantity rather than a probability-based property of the nature. Information is a general form of abstract objects represented by symbolical, mathematical, communication, computing, and cognitive systems. Therefore, information science is one of the contemporary scientific disciplines collectively known as abstract sciences such as system, information, cybernetics, cognition, knowledge, and intelligence sciences. This paper presents the cognitive foundations, mathematical models, and formal properties of information towards an extended theory of information science. From this point of view, information is classified into the categories of classic, computational, and cognitive information in the contexts of communication, computation, and cognition, respectively. Based on the three generations of information theories, a coherent framework of contemporary information is introduced, which reveals the nature of information and the fundamental principles of information science and engineering.
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1. Introduction

It is recognized that information is a general form of abstract objects perceived by human brains and represented by symbolical, mathematical, communication, computing, and cognitive systems. Therefore, information is one of the essences of the physical and abstract worlds among matter, energy, and intelligence. Information science is one of the contemporary scientific disciplines beyond the traditional natural, engineering, and social sciences, which are collectively known as abstract science or science of sciences such as system, information, cybernetics, cognition, knowledge, intelligence sciences in addition to mathematics, logic, and philosophy. They are abstract science in common because human knowledge in nature is a multi-layer hierarchical structure where only the lower-layer of knowledge is directly related to the material world.

The concept of information may be traced back to the work of Hartley, Shannon, Weaver, Bell, Goldman, and Ash during the 1920s to 1950s [Hartley, 1928; Shannon, 1948; Shannon and Weaver, 1949; Bell, 1953; Goldman, 1953; Ash, 1956]. Since then, information has been perceived quite diversely in sciences, engineering, society, and everyday lives. Typical perceptions on information have been such as communication signals, probable channel properties, messages, entropy, states, relations, knowledge, data, sensorial inputs, perceptions, semantics, reasoning products, and thinking threads [Gray, 1990; Zadeh, 1997; Wilson & Frank, 2001; Skowron & Stepaniuk, 2001; Cover & Thomas, 2006; Belkin & Robertson, 2007, Zhong, 2013; Wang, 2002, 2003, 2006, 2007b, 2012a; Wang & Fariello, 2012; Wang et al., 2009a, b, 2010].

The role and nature of information can be elaborated by the universe of discourse of humanity (UDH) [Wang, 2003; Wang et al., 2006], which reveals that the natural world is a dual encompassing both the physical world (PW) and the abstract world (AW) as shown in Figure 1. There are four essences for modeling the natural world (NW) in UDH known as matter (M), energy (E), information (I), and intelligence (). Therefore, UDH can be denoted by the information-matter-energy-information-intelligence (MEII) model with the four essences of the natural world (NW).

Figure 1.

The MEII model of the universe of discourse of humanity (UDH)

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