By V. Kulish

The e-book comprises Volumes. the 1st (the previous quantity) is dedicated to the overall nonlinear thought of the hierarchical dynamic oscillative–wave structures. This idea has been known as the idea of hello- archical oscillations and waves. right here elements of the proposed thought are mentioned. the 1st points situation the elemental nature and the elemental c- cepts and ideas of a brand new hierarchical method of learning hierarchical dynamic structures. a brand new hierarchical paradigm is proposed as a - sis of a brand new perspective of such sorts of platforms. In flip, a collection of hierarchical ideas is formulated because the basic foundation of this paradigm. Therein the self-resemblance (holographic) precept performs a key position right here. An enough mathematic description (factorization) of the proposed paradigm is performed. The recommendations of structural and dynamic (functional) operators are placed into the root of this descr- tion. Electrodynamics is selected as a handy foundation for an noticeable demonstration of a few key issues of the proposed new concept. the second one element has a simply mathematical nature. it truly is regarding the shape of factorization (i.e., mathematical description) of hier- chical different types of dynamic versions, and dialogue of the equipment in their mathematical research. a suite of the hierarchical asymptotic analytical– numerical tools is given as a proof of the sensible effectiveness of the proposed model of hierarchical conception.

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Nevertheless, these and other approaches mentioned in this section possess a number of important shortcomings as concerns applying formal methods to the design of NLPSs and to developing the theory of NLPSs. The demands of diverse application domains to the formal means for describing natural language may differ. That is why we distinguish for further analysis the following groups of application domains: • Natural-language interfaces to databases, knowledge bases, autonomous robots. , in particular, intelligent text summarization systems.

In particular, there are no adequate formal means to describe on semantic level the operations with the sets. It appears that the collection of restrictions stated above provides a useful reference-point for enriching the stock of the means and models for the mathematical study of NL-communication. 7 The Significance of Highly Expressive Formal Systems of Semantic Representations The collection of the tasks faced by the theory of semantics-oriented linguistic processors (LPs) in the beginning of the 1980s proved to be extremely complicated.

A broadly applicable mathematical model of a linguistic database, that is, a model of a collection of semantic-syntactic data associated with primary lexical units and used by the algorithms of semantic-syntactic analysis for building semantic representations of natural language texts (see Chap. 7 of this book). 8. A new method of transforming an NL-text (a statement, a command, or a question) into its semantic representation (see Chap. 8 of this book). 9. Two complex, strongly structured algorithms of semantic-syntactic analysis of NL-texts (they possess numerous common features).