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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...
The fuzzy nature of language structures and semantics is formally studied towards a methodology for reasoning with fuzzy concepts (RFC). Mathematical models of fuzzy concepts and fuzzy semantics are introduced based on concept algebra and semantic algebra. The semantic effects of fuzzy modifiers and quantifiers on fuzzy concepts are quantitatively analyzed. Experiments on collective intension and...
The fuzzy and algebraic treatment of the hyperstructured logical variables and complex logical expressions are centric in inference methodologies of many contemporary disciplines such as cognitive informatics, cognitive computing, computational linguistics, cognitive semantics, causal inferences, computing with words, cognitive robotics, and computational intelligence. This paper presents a denotational...
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...
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