1. Kherson, May 20-22, 20091 Nikolaj S. Nikitchenko Kyiv National Taras Shevchenko University, Ukraine Integration of Informatics-Programming Disciplines on a Base of Composition Nominative Approach

2. Kherson, May 20-22, 20092 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

3. Kherson, May 20-22, 20093 Specialization-Integration Cycle in Theories Development Integration Specialization

4. Kherson, May 20-22, 20094 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?

5. Kherson, May 20-22, 20095 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.

6. Kherson, May 20-22, 20096 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)

7. Kherson, May 20-22, 20097 Levels of notions and their orientation on the Sphere of Computing Practice Theory Society Transportati on … … … Sphere of Education Computing (Informatization) Categories Scientific notions Formal notions Levels: Philosophical, Scientific, Mathematical

8. Kherson, May 20-22, 20098 Types of Notions  categories  scientific notions  formal notions

9. Kherson, May 20-22, 20099 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.

10. Kherson, May 20-22, 200910 Operations over Notions  Projection: Categories  Scientific Notions  Formalization: Scientific Notions  Formal Notions

11. Kherson, May 20-22, 200911 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)

12. Kherson, May 20-22, 200912 Expected Results  Net of Notions (Ontology)  on various levels  with relations between them Philosophical Scientific Mathematical

13. Kherson, May 20-22, 200913 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

14. Kherson, May 20-22, 200914 Profile of the use of terms “Knowledge”, “Information”, and “Data” Content Form Knowledge InformationData

15. Kherson, May 20-22, 200915 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)

16. Kherson, May 20-22, 200916 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)

17. Kherson, May 20-22, 200917 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

18. Kherson, May 20-22, 200918 Descriptive Pentad for Information Process naming (nomination) INFORMATION PROCESS NAME Semantic aspect Syntactical aspect application interpretation grammar Denotational aspect DESCRIPTION COMPOSITION

19. Kherson, May 20-22, 200919 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

20. Kherson, May 20-22, 200920 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.

21. Kherson, May 20-22, 200921 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

22. Kherson, May 20-22, 200922 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

23. Kherson, May 20-22, 200923 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

24. Kherson, May 20-22, 200924 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.

25. Kherson, May 20-22, 200925 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.

26. Kherson, May 20-22, 200926 Conclusion The 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

27. Kherson, May 20-22, 200927 Thank you! Questions?