Kherson, May 20-22, 2009 1

Nikolaj S. Nikitchenko

Kyiv National Taras Shevchenko University, Ukraine

Integration of Informatics-Programming

Disciplines on a Base of Composition Nominative Approach

Kherson, May 20-22, 2009 2

Introduction

Students lack a unified view on informatics (computer science)

We will advocate necessity of integrative approach to informatics-programming disciplines (disciplines “around” programming) and present its main methodological aspects and basic notions

Kherson, May 20-22, 2009 3

Specialization-Integration Cycle in Theories Development

Integration

SpecializationSpecialization

Specialization

SpecializationSpecialization

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Integration of Theories

Traditionally integration means constructing of more general theory or mutual translation of theories

Here integration means to present informatics as a whole having various interconnected aspects and parts

How to achieve this goal?

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Methodological Principles Principle of universal connection: everything is

connected with something else.

Principle of development from abstract to concrete: development is definitely oriented change of the object (notion) from abstract to concrete (from simple to complex, from a lower level to a higher one).

Principle of triadic development: one of the main schemes of development is specified as a development triad

thesis – antithesis – synthesis.

Principle of unity of theory and practice: theory and practice should be considered as influencing each other.

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Main Aspects of Subject-Object Relation

Gnoseological (how to cognate the object) Ontological (what parts object consists of) Phenomenological (how the object presents itself

to the subject)

Praxiological (how to work with the object)

Main aspects in the approach: gnoseological and praxiological (theory and practice)

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Levels of notions and their orientation on the Sphere of Computing

Practice

Theory

Society

Transportation

… … …

Sphere of Education

Computing(Informatization)

Categories

Scientific notions

Formal notions

Levels:

Philosophical,

Scientific,

Mathematical

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Types of Notions

categories

scientific notions

formal notions

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Examples of Categories subject and object; abstract and concrete; internal and external; quality, quantity, and measure; essence and phenomenon; individual, general, and particular; whole and part; content and form; cause and effect; etc.

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Operations over Notions

Projection: Categories Scientific Notions

Formalization:Scientific Notions Formal Notions

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Slogan of the Approach (methodological level)

Integrity By Development From Abstract to Concrete From Philosophical via

Scientific to Mathematical Level

(vertical integrity) With Integrity on each Level

(horizontal integrity)

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Expected Results

Net of Notions (Ontology)

on various levels

with relations between them

Philosophical

Scientific

Mathematical

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Developing Scientific Notions Categories are developed in Philosophy

We develop Scientific Notions

The main notion: information Information:

knowledge presented via external form (that can be stored, copied, proceed, etc.)

Information: projection of categories “form and content”

Data: a form of information

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Profile of the use of terms “Knowledge”, “Information”, and “Data”

Content Form

Knowledge

Information Data

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Definition of Informatics (first approximation)

Informatics: science that studies - information processing

- by algorithmic methods- with the use of computers

Three aspects of informatics:- information processing in general- constructivity of such processing- practical realization (with computers)

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The notion of Language

Developed forms of information, information processing, and their aspects are based on the notion of language

Our slogan (on scientific level):the main notion of informatics is the notion of language (primarily in constructive, formal, communicative, and practical aspects)

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Developing the Notion of Information Process (descriptive aspect)

Two steps of developments: the triad:

information – information process – name the pentad

information – information process – name –

composition – description

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Descriptive Pentad for Information Process

naming (nomination)

INFORMATION

PROCESS

NAME

Semantic aspectSyntactical aspect

application

interpretation

grammar

Denotational aspect

DESCRIPTION

COMPOSITION

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Formalizing the Notion of Language (internal aspects)

Language: Semantic System (Composition System) Syntactical System Denotational System

Our slogan (on mathematical level):the first language models –

Composition Nominative Models

Composition System: Data – Function – Composition

Models of Data Processing Languages

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Developing the notion of Data

This notion is developed according to the following triads of categories:

whole (W) – parts (P) – synthesis (H as Hierarchy) abstract (A) – concrete (C) – synthesis (S).

Thus, we get 9 levels of data types.

Data structures used in informatics can be specified as concretizations of the considered types of data.

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Diagram of development of the notion of data

… … …

DATA

Level W (Whole)

Level P (Parts)

Level S(Hierarchy)

P.C – sets

P.S – nominative data (nominats)

H.A

W.A –“black box” W.C –“white box”

P.A – presets

H.C

H.S

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Nominative Data Types The typology of nominats is based on the

fundamental relation name value

(the first relation of knowledge representation)

Three dichotomies:

- simple values – complex values- simple names – complex names- values are not names – values as names

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Cube of Nominates Types

Values as Names

Complex Names

Complex Values

Values not Names

Simple Names

Simple Values

Example: A[i,j+1] – complex names, values as names

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Formalizing the main notions The constructed hierarchical system of notions

is a subject for formalization on a basis of the formulated methodological principles.

In particular, the notions of information and data processes can be formalized as a composition nominative system which consists of semantic, syntactic and denoting systems.

Such systems formalized languages used in programming, computability theory, algebra, and mathematical logic.

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References

Formal definitions are presented in: Nikitchenko N.S. A Composition Nominative

Approach to Program Semantics.– IT-TR: 1998-020.– Technical University of Denmark.– 1998.– 103 p.

Нікітченко М.С., Шкільняк С.С. Математична логіка та теорія алгоритмів: підручник.– К.: ВПЦ «Київський університет», 2008.– 528 с.

Nikitchenko N.S. Abstract Computability of Non-deterministic Programs over Various Data Structures. LNCS, vol. 2244, Springer 2001.– P. 468–481.

Басараб И.А., Никитченко Н.С., Редько В.Н. Композиционные базы данных. –К.: Либідь, 1992. – 191 с.

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ConclusionThe proposed approach seems to be useful in

teaching due to the following: it presents an integrated view on informatics and

corresponding disciplines it is based on a small number of principles thus

specifying a clear structure of informatics it proposes various abstraction levels starting from

simple to more elaborate presenting more complex concepts on later stages of education

The main notions are formalized that permits to construct corresponding software systems

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Thank you!Questions?