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Mathematical byways in Ayling, Beeling and Ceeling by Hugh ApSimon

By Hugh ApSimon

Specified and hugely unique, Mathematical Byways is a piece of leisure arithmetic, a suite of creative difficulties, their much more inventive recommendations, and extensions of the problems--left unsolved here--to extra stretch the brain of the reader. the issues are set in the framework of 3 villages--Ayling, Beeling, and Ceiling--their population, and the relationships (spacial and social) among them. the issues may be solved with little formal mathematical wisdom, even supposing so much require huge suggestion and psychological dexterity, and options are all essentially expounded in non-technical language. Stimulating and weird, this booklet proves what Hugh ApSimon has identified all alongside: arithmetic should be enjoyable!

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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).

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