A formal model for constructing semantic expansions of the search requests about the achievements and failures
The paper describes a new method of constructing recommender systems with natural-language interface. This method is based on the theory of K-representations (knowledge representations) - a new theory of designing semantic-syntactic analyzers of natural language texts with the broad use of formal means for representing input, intermediary, and output data. The current version of the theory is set forth in a monograph (the author is V.A. Fomichov) published by Springer in 2010. The stated approach is implemented in the programming environment PHP + MySQL: an experimental recommender system has been developed.
A comprehensive theoretical framework for the development of a Semantic Web of a new generation, or of a Multilingual Semantic Web, is outlined. Firstly, the paper grounds the possibility of using a mathematical model being the kernel of the theory of K-representations and describing a system of 10 partial operations on conceptual structures for building semantic representations (or text meaning representations) of, likely, arbitrary sentences and discourses in English, Russian, French, German, and other languages. The possibilities of using SK-languages defined by the theory of K-representations for building semantic annotations of informational sources and for constructing semantic representations of discourses pertaining to biology and medicine are illustrated. Secondly, an original strategy of transforming the existing Web into a Semantic Web of a new generation with the well-developed mechanisms of understanding natural language texts is described. The third subject of this paper is a description of the correspondence between the inputs and outputs of the elaborated algorithm of semantic-syntactic analysis and of its advantages; the semantic representations of the input texts are the expressions of SK-languages (standard knowledge languages). The input texts can be the statements, questions, and commands from the sublanguages of English, Russian, and German. The algorithm has been implemented by means of the programming language PYTHON.
The first starting point of this paper is the broadly accepted idea of employing, as a promising methodology, an artificial semantic language-intermediary for the realization of automatic cross-lingual intelligent information access to natural language (NL) texts on the Web. The second one is the emergence in computational semantics during 2013-2016 of great interest in the semantic formalism (more exactly, notation) called Abstract Meaning Representation (AMR). This formalism was introduced in 2013 in an ACL publication by a group consisting of ten researchers from UK and USA. This paper shows that much broader prospects for creating semantic languages-intermediaries in comparison with AMR are opened by the theory of K-representations (TKR), developed by V. A. Fomichov. The basic mathematical model of TKR describes the regularities of NL structured meanings. The mathematical essence is that this model introduces a system consisting of ten partial operations on conceptual structures. Initial version of this model was published in 1996 in Informatica (Slovenia). The second version of the model (stated in a monograph released by Springer in 2010) defines a class of formal languages called SK-languages (standard knowledge languages). It is demonstrated that SK-languages allow us to simulate all expressive mechanisms of AMR. The advantages in comparison with AMR are, in particular, the possibilities to construct semantic representations of compound infinitive constructions (expressing goals, commitments, etc), of compound descriptions of notions and sets, and of complex discourses and knowledge pieces.
The paper describes a new method of constructing semantic expansions of search requests about the achievements and failures of active systems (organizations, people) for improving the results of Web search. This method is based on the theory of K-representations (knowledge representations), proposed by V.A. Fomichov - a new theory of designing semantic-syntactic analysers of natural language texts with the broad use of formal means for representing input, intermediary, and output data. The method uses an original formal model of a goals base – a knowledge base containing the information about the goals of active systems. The stated approach is implemented with the help of the Web programming language Java: an experimental search system AOS (Aspect Oriented Search) has been developed and tested.
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables