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Formal semantic theories underpin a wide range of methodologies in knowledge science, cognitive linguistics, machine learning, and cognitive computing. This paper presents a set of mathematical rules for rigorous concept and semantics manipulations. Mathematical models of the universe of discourse of knowledge, semantic space and formal concepts are created. The formal properties of knowledge are...
Semantic comprehension is a fundamental challenge to machine learning. A methodology for building quantitative semantic hierarchies of formal concepts is formally described by cognitive machine learning. The algorithm of concept semantic hierarchy learning (CSH_Learning) is developed based on a set of semantic analysis and synthesis rules according to concept algebra. The algorithm and rules are applied...
An ontology is a taxonomic hierarchy of lexical terms and their syntactic and semantic relations for representing a framework of structured knowledge. Ontology used to be problem-specific and manually built due to its extreme complexity. Based on the latest advances in cognitive knowledge learning and formal semantic analyses, an Algorithm of Formal Ontology Generation (AFOG) is developed. The methodology...
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...
Concept elicitation is centric for machine knowledge extraction and representation in cognitive robot learning. This paper presents a supervised methodology for machine concept elicitation from informal counterparts described in natural languages. The collective opinions of a given concept in ten selected dictionaries are quantitatively analyzed and formally represented according to the attribute-object-relation...
It is recognized that the semantic space of knowledge is a hierarchical concept network. This paper presents theories and algorithms of hierarchical concept classification by quantitative semantic relations via machine learning based on concept algebra. The equivalence between formal concepts are analyzed by an Algorithm of Concept Equivalence Analysis (ACEA), which quantitatively determines the semantic...
Concept elicitation is a fundamental methodology for knowledge extraction and representation in cognitive robot learning. Traditional machine learning technologies deal with object identification, cluster classification, functional regression, and behavior acquisition. This paper presents a supervised machine knowledge learning methodology for concept elicitation from sample dictionaries in natural...
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...
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, intelligence, and systems. New forms of mathematics are sought, collectively known as denotational mathematics, in order to deal with complex mathematical...
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...
The denotational and expressive needs in cognitive informatics, computational intelligence, software engineering, and knowledge engineering lead to the development of new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of mathematical structures that formalize rigorous expressions and long-chain inferences of system compositions and behaviors...
Concept algebra is a denotational mathematics for rigorously manipulating formal concepts and their algebraic operations in knowledge representation, semantic analyses, and machine learning. Properties of concept algebra are formally studied in order to elaborate the nature of formal concepts and their algebraic operations. This leads to a set of algebraic rules in the categories of relational, reproductive,...
Semantics is the meaning of a language unit at the levels of word, phrase, sentence, paragraph, and essay. Cognitive linguistics focuses on cognitive semantics of sentences and its interaction with syntactic structures. A denotational mathematical framework of language semantics known as semantic algebra is developed in this paper. Semantic algebra reveals the nature of semantics by a general mathematical...
Cognitive linguistics is an emerging discipline that studies the cognitive properties of natural languages and the cognitive models of languages in computational linguistics, cognitive computing, and computational intelligence. This paper presents the theoretical framework of cognitive linguistics in order to systematically formalize the syntaxes and grammars of natural languages. An abstract language...
The cognitive complexity of texts in natural languages is a fundamental measure of the properties of syntax and semantics in textual comprehension, processing, and search. This paper presents a formal metrics of text comprehension complexity in cognitive linguistics. Both objective and subjective aspects of text comprehension and their complexity are formally modeled. A formal language model is established...
The contemporary wonder of sciences and engineering has recently refocused on the starting point of them: How the brain processes internal and external information autonomously and cognitively rather than imperatively as those of conventional computers do? This leads to the advances in the field of Cognitive Informatics (CI) as a transdisciplinary enquiry of computer science, information sciences,...
Concept Algebra (CA) is a denotational mathematical structure for formal knowledge representation and manipulations in cognitive computing and machine learning. CA provides a rigorous and dynamic knowledge modeling and processing tool, which extends the informal, static, and application-specific ontological technologies. An operational semantics for the calculus of CA is formally elaborated using...
Knowledge representation is one of the central problems in the design and implementation of a cognitive learning engine (CLE). A formal knowledge representation system (FKRS) is developed for autonomous concept formation based on concept algebra. The object-attribute-relation (OAR) model for knowledge representation is adopted in the design of FKRS. The conceptual model, architectural model, and behavioral...
The contemporary wonder of sciences and engineering has recently refocused on the beginning point of them: how the brain processes internal and external information autonomously and cognitively rather than imperatively as those of conventional computers. Cognitive Informatics (CI) is a transdisciplinary enquiry of computer science, information sciences, cognitive science, and intelligence science...
It is recognized that the key theoretical and technical problems toward the next generation internet are not only a speed issue, but also a more fundamental issue of the increasingly demands for the sharing of computational intelligent capabilities. According to cognitive informatics, the cognitive information that humans acquire, process, retain, and share can be classified into four profound forms...
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