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Über dieses Buch

Gluecklich, die wissen, dass hinter allen Sprachen das Unsaegliche steht. Those are happy who know that behind all languages there is something unsaid Rainer Maria Rilke This book shows in a new way that a solution to a fundamental problem from one scienti?c ?eld can help to ?nd the solutions to important problems emerged in several other ?elds of science and technology. In modern science, the term “Natural Language” denotes the collection of all such languages that every language is used as a primary means of communication by people belonging to any country or any region. So Natural Language (NL) includes, in particular, the English, Russian, and German languages. The applied computer systems processing natural language printed or written texts (NL-texts) or oral speech with respect to the fact that the words are associated with some meanings are called semantics-oriented natural language processing s- tems (NLPSs). On one hand, this book is a snapshot of the current stage of a research p- gram started many years ago and called Integral Formal Semantics (IFS) of NL. The goal of this program has been to develop the formal models and methods he- ing to overcome the dif?culties of logical character associated with the engineering of semantics-oriented NLPSs. The designers of such systems of arbitrary kinds will ?nd in this book the formal means and algorithms being of great help in their work.



Part I A Comprehensive Mathematical Framework for the Development of Semantic Technologies

Chapter 1. Mathematical Models for Designing Natural Language Processing Systems as a New Field of Studies for Systems Science

This chapter grounds the necessity of developing new mathematical tools for the design of semantics-oriented natural language processing systems (NLPSs) and prepares the reader to grasping the principal ideas of these new tools introduced in the next chapters. Section 1.1 grounds the expedience of placing into the focus of Systems Science the studies aimed at constructing formal models being useful for the design of semantics-oriented NLPSs. Sections 1.2, 1.3, and 1.4 contain the proposals concerning the structure of such mathematical models of several new types that these models promise to become a great help to the designers of semantics-oriented NLPSs. Sections 1.5 and 1.6 jointly give the rationale for the proposed structure of new mathematical models. Section 1.5 states the central ideas of Cognitive Linguistics concerning natural language (NL) comprehension. Section 1.6 describes the early stage of the studies on formal semantics of NL. Section 1.7 sets forth the idea of developing formal systems of semantic representations with the expressive power close to that of NL; this idea is one of the central ones for this monograph.

Vladimir A. Fomichov

Chapter 2. Introduction to Integral Formal Semantics of Natural Language

This chapter sets forth the basic ideas and components of Integral Formal Semantics (IFS) of Natural Language – a many-component branch both of formal semantics of NL and Computer Science developed by the author of this book. Section 2.1 describes the basic principles of IFS and introduces the notion of a broadly applicable conceptual metagrammar. Section 2.2 shortly characterizes the principal components of IFS. Sections 2.3, 2.4, 2.5, 2.6, and 2.7 describe a number of the principal components of IFS. These sections contain numerous examples reflecting the different stages of elaborating powerful and flexible formal means for describing semantic structure of NL-texts – sentences and discourses.

Vladimir A. Fomichov

Chapter 3. A Mathematical Model for Describing a System of Primary Units of Conceptual Level Used by Applied Intelligent Systems

The first section of this chapter formulates a problem to be solved both in Chaps 3 and 4: it is the problem of describing in a mathematical way the structured meanings of a broad spectrum both of sentences and discourses in natural language. The second section states a subproblem of this problem, it is the task of constructing a mathematical model describing a system of primary units of conceptual level and the information associated with such units and needed for joining the primary units with the aim of building semantic representations of arbitrarily complicated Natural Language texts. A solution to this task forms the main content of this chapter. From the mathematical standpoint, the proposed solution is a definition of a new class of formal objects called conceptual bases.

Vladimir A. Fomichov

Chapter 4. A Mathematical Model for Describing Structured Meanings of Natural Language Sentences and Discourses

The purpose of this chapter is to construct a mathematical model describing a system consisting of ten partial operations on the finite sequences with the elements being structured meanings of Natural Language (NL) expressions. Informally, the goal is to develop a mathematical tool being convenient for building semantic representations both of separate sentences in NL and of complex discourses of arbitrary big length pertaining to technology, medicine, economy, and other fields of professional activity. The starting point for developing this model is the definition of the class of conceptual bases introduced in the previous chapter. The constructed mathematical model includes the definition of a new class of formal systems, or calculuses – the class of K-calculuses (knowledge calculuses) and the definition of a new class of formal languages – the class of SK-languages (standard knowledge languages).

Vladimir A. Fomichov

Chapter 5. A Study of the Expressive Possibilities of SK-Languages

In this chapter we will continue the analysis of the expressive possibilities of SK-languages. The collection of examples considered above doesn’t demonstrate the real power of the constructed mathematical model. That is why let’s consider a number of additional examples in order to illustrate some important possibilities of SK-languages concerning the construction of semantic representations of sentences and discourses and describing the pieces of knowledge about the world. The advantages of the theory of SK-languages in comparison, in particular, with Discourse Representation Theory, Episodic Logic, Theory of Conceptual Graphs, and Database Semantics of Natural Language are set forth. If the string


of a certain SK-language is a semantic representation of a natural language expression


, the string


will be called

a possible K-representation (KR) of the expression T


Vladimir A. Fomichov

Chapter 6. The Significance of a New Mathematical Model for Web Science, E-science, and E-commerce

The significance of the theory of K-representations for e-science, e-commerce, and Web science is shown. The following possibilities provided by SK-languages are analyzed: building semantic annotations of Web-sources and Web-services, constructing high-level conceptual descriptions of visual images, semantic data integration, and the elaboration of formal languages intended for representing the contents of messages sent by computer intelligent agents (CIAs). It is also shown that the theory of SK-languages opens new prospects of building formal representations of contracts and records of commercial negotiations carried out by CIAs. A theoretically possible strategy of transforming the existing Web into Semantic Web of a new generation is proposed.

Vladimir A. Fomichov

Part II FormalMethods and Algorithms for the Design of Semantics-Oriented Linguistic Processors

Chapter 7. A Mathematical Model of a Linguistic Database

In this chapter a broadly applicable mathematical model of linguistic database is constructed, 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.

Vladimir A. Fomichov

Chapter 8. A New Method of Transforming Texts into Semantic Representations

This chapter sets forth a new method of describing the transformation of an NL-text (a statement, a command, or a question) into its semantic representation. According to this method, the transformation includes three phases: (a) Phase 1: The component-morphological analysis of the text; (b) Phase 2: The construction of a matrix semantic-syntactic representation (MSSR); (3) Phase 3: The assembly of a semantic representation of the text, proceeding from its MSSR.

Vladimir A. Fomichov

Chapter 9. Algorithm of Building a Matrix Semantic-Syntactic Representation of a Natural Language Text

This chapter sets forth an original algorithm of constructing a matrix semantic-syntactic representation of a natural language text. This algorithm, called


1, is multilingual: the input texts (the statements, commands, and questions) may belong to the sublanguages of English, German, and Russian languages (a Latin transcription of Russian texts is considered). A pure syntactic representation of an analyzed text isn’t used: the proposed algorithm is oriented at directly finding the conceptual relations between the meanings of the fragments of an NL-text.

Vladimir A. Fomichov

Chapter 10. An Algorithm of Semantic Representation Assembly

An algorithm transforming a matrix semantic-syntactic representation


of a natural language text into a formal expression





), where


is the conceptual basis being the first component of the used marked-up conceptual basis


, and




) is the SK-language in the basis


, was called above

an algorithm of semantic assembly

. This chapter describes (a) an algorithm of semantic assembly


1, (b) an algorithm of semantic-syntactic analysis


1 being the composition of the algorithms


1 and



Vladimir A. Fomichov

Chapter 11. Natural Language Processing Applications

The principles of applying the theory of K-representations to the design of two semantics-oriented natural language processing systems are set forth. The first one is the computer system Mailagent1; the task to be solved by this system is semantic classification of e-mail messages stored in the user’s mailbox for enabling the user to more quickly react to the more important and/or urgent messages. The second system is the linguistic processor NL-OWL1 transforming the descriptions in restricted Russian language of situations (in particular, events) and the definitions of notions first into the K-representations and then into the OWL-expressions.

Vladimir A. Fomichov


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