Papers by Mykola Nikitchenko
Renominative logics with extended renomination, equality and predicate complement
<jats:p>A new class of program-oriented logical formalisms is investigated – renominative l... more <jats:p>A new class of program-oriented logical formalisms is investigated – renominative logics with extended renominations, equality predicates, and predicate complement composition. Composition algebras and languages of such logics are described; their semantic properties are investigated. For these logics, a number of logical consequence relations are proposed and investigated, in particular, the logical consequence relations with undefinedness conditions. Properties of these relations form the semantic basis for further construction of sequent-type calculi for the proposed logics.</jats:p>
Cybernetics, 1988
In order to formalize the computability of a function over finite structure data, we first need t... more In order to formalize the computability of a function over finite structure data, we first need to define such data. This is a difficult question, and we will accordingly adopt the following strategy: we will first define a special form of finite structure data and subsequently reduce data of other forms to this special form. The intuitive notion of finite structure data is the following: any datum d consists of several components bz, .... b m organized in a certain way. If there are denumerably many different forms of organization for finite structure data, each of these data can be represented in the (possibly nonunique) form (k, <bz,...,bm>), where k is the datum code and the sequence <b I .... ,bm> is the datum base. Data of this form are called natural data [41]. Definition 4. Let B be a set. Then the set of natural data over B is the set N_B = Nat • B e. Therefore, we treat the set of data D as the set of finite structure data if there are given set B and an everywhere defined injective mapping nat:D + N_B. This mapping will be called the naturalization mapping, and the partial inverse mapping nat-Z:N_B + D will be called the denaturalization mapping denat. (The case of many-valued naturalization mappings is not considered here.) The introduction of natural data and naturalization mappings enables us to reduce computability over D to special computability over N_B, which is called proper computability [41]. The computability over D obtained in this way is called natural computability, according to the following definition. Definition 5. The function r: D I%D is called naturally computable (with respect to given mappings nat and denat) if there exists a properly computable function g: N_B~N_B such that f = natogo denat. In order to complete the definition of natural computability over D, we have to define proper computability over N_B. This computability is independent of any specific processing tools of the elements of the set B, i.e., it uses only its own tools independent of B. Therefore the datum code plays a major role, and the elements of the datum base are "extras" that virtually do not affect the computations. Definition 6. The function g:N_B-~N_B is called properly computable if there exists a partially recursive many-valued functions h:Nat-~Nat(Nat *) such that
Information and Communication Technologies in Education, Research, and Industrial Applications: 11th International Conference, ICTERI 2015, Lviv
Springer eBooks, Dec 5, 2013
ICT in Education, Research, and Industrial Applications: 8th International Conference, ICTERI 2012, Kherson, Ukraine, June 6-10, 2012, Revised
Springer eBooks, Jan 11, 2013
This book constitutes the refereed proceedings of the 8th International Conference on ICT in Educ... more This book constitutes the refereed proceedings of the 8th International Conference on ICT in Education, Research, and Industrial Applications, held in Kherson, Ukraine, in June 2012. The 14 revised full papers were carefully reviewed and selected from 70 submissions. This book begins with an invited contribution presenting the substance of one of ICTERI 2012 invited talks. The chapter deals with the issues of abstraction and verification of properties in real-time Java programs. The rest of the volume is structured in four topical parts: ICT Frameworks, Infrastructures, Integration, and Deployment; Formal Logic and Knowledge-Based Frameworks; ICT-Based Systems Modeling, Specification, and Verification: ICT in Teaching and Learning.
Cybernetics and Systems Analysis, 1993
Problemy programmirovaniâ, 2016
Запропоновано поняття квазіарної реляції (відношення), введено операції над такими реляціями, опи... more Запропоновано поняття квазіарної реляції (відношення), введено операції над такими реляціями, описано алгебри квазіарних реляцій. Доведено ізоморфізм алгебри квазіарних реляцій та першопорядкової алгебри тотальних однозначних квазіарних предикатів. Побудовано алгебри бі-квазіарних реляцій, задані на множинах пар квазіарних реляцій. Визначено різні підкласи таких алгебр та досліджено їх зв'язки з алгебрами часткових однозначних, тотальних неоднозначних, часткових неоднозначних, монотонних, антитонних квазіарних предикатів. Ключові слова: алгебра, логіка, ізоморфізм, реляція, квазіарний предикат.
Composition Models of Databases
Workshops in computing, 1995
Special models of databases are constructed based on principles of composition programming. The d... more Special models of databases are constructed based on principles of composition programming. The determinacy, subordination and separation principles define a semantic-syntactic style of approach proposed, and the naming, functionality and compositionality principles define the algebraic method of formalization of informational and manipulational aspects. The informational model is considered to be the special subclass of named data, satisfying integrity constraints, and the manipulational model is defined by sets of basic manipulational functions and compositions. Computational completeness of the constructed models for general classes of named data, tabular and quasirelational data is studied.
Cybernetics and Systems Analysis, 1991
Characteristics of Educational Standard Development in Informatics (Training Direction 0403020)
Ìnformacìjnì tehnologìï v osvìtì, May 31, 2010
Abstract Computability of Non-deterministic Programs over Various Data Structures
Springer eBooks, 2001
Partial multi-valued functions represent semantics of nondeterministic programs. The notion of na... more Partial multi-valued functions represent semantics of nondeterministic programs. The notion of naturally computable partial multi-valued function is introduced and algebraic representations of complete classes of naturally computable functions over various data structures are constructed.
Abstract Transport Systems: An Initial Study
Information and Communication Technologies in Education, Research, and Industrial Applications
Communications in computer and information science, 2013
Researchers, policy-makers, and industry practitioners alike herald the Knowledge-Based Bio-Econo... more Researchers, policy-makers, and industry practitioners alike herald the Knowledge-Based Bio-Economy (KBBE) as the “Next Big Thing” in societal progress. The story, which receives a lot of attention, goes like this: Over the last decades, economies around the globe have transformed into a Knowledge-Based Economy (KBE). Knowledge became the Economy-Defining Resource (EDR) of the KBE and Information and Communication Technology (ICT) has served as its Economy-Defining Technology (EDT). Now modern biotechnology becomes another EDT – leading to the KBBE. Bio-resources jointly with knowledge take on the role of the KBBE EDRs. At the heart of this story lies the relationship between resources, technologies and economies, which, under distinct circumstances, may give rise to a major economic transformation. This raises a number of important questions: What constitutes the implied primacy of economics? Why is the KBBE the next big thing? What is the role of resources, namely knowledge and bio-resources, in the context of economic transformations? Why are ICT and biotechnology the EDTs for these economic transformations? With respect to the KBBE, what are the enabling technologies? Last but not least, given the overall ICTERI conference theme and given that ICT remains an EDT for the KBBE, what are the high-level and long-term KBBE ICT challenges? The paper discusses these challenges and attempts to answer these questions at a conceptual level.
ICTERI, 2012
We investigate algorithms for solving the satisfiability problem in composition-nominative logics... more We investigate algorithms for solving the satisfiability problem in composition-nominative logics of quantifier-equational level. These logics are algebra-based logics of partial predicates constructed in a semantic-syntactic style on the methodological basis, which is common with programming; they can be considered as generalizations of traditional logics on classes of partial predicates that do not have fixed arity. We show the reduction of the problem in hand to the satisfiability problem for classical first-order predicate logic with equality. The proposed reduction requires extension of logic language and logic models with an infinite number of unessential variables. The method developed in the paper enables us to use existent satisfiability checking procedures also for quantifier composition-nominative logic with equality.
Composition Models of Object-Oriented Databases
Advances in Databases and Information Systems, 1994
Cybernetics and Systems Analysis, Mar 1, 2000
Compositions of partial predicates of the highest abstraction level that form the basis of ii!fhl... more Compositions of partial predicates of the highest abstraction level that form the basis of ii!fhlital3' propositional logics are defined and investigated. The compositions are completely described in terms of special algebras called Kleene algebras, and a complete system of identities is constructed for such compositions.
Problemy programmirovaniâ, 2017
Вивчаються чистi першопорядковi квазіарні логіки однозначних та неоднозначних часткових предикаті... more Вивчаються чистi першопорядковi квазіарні логіки однозначних та неоднозначних часткових предикатів. Основна увага приділена таким логікам із спеціальними предикатами рівності. Виділено чистi першопорядковi логіки з предикатами слабкої рівності та з предикатами строгої рівності. Описано мови та семантичні моделі цих логік, досліджено їх семантичні властивості, зокрема, властивості, пов'язані з предикатами рівності. Наведено властивості відношень логічного наслідку для множин формул. На базі цих властивостей для чистих першопорядкових логік з предикатами рівності побудовано низку числень секвенційного типу, для них доведено теореми коректності та повноти. Ключові слова: логіка, предикат, рівність, логічний наслідок, секвенційне числення.
Teaching Theory of Programming: Methodology and Basic Notions
Information Technologies in Education, 2008
PROBLEMS IN PROGRAMMING, 2016
Pure first-order logics of partial and total, single-valued and multi-valued quasiary predicates ... more Pure first-order logics of partial and total, single-valued and multi-valued quasiary predicates are investigated. For these logics we describe semantic models and languages, giving special attention in our research to composition algebras of predicates and interpretation classes (sematics), and logical consequence relations for sets of formulas. For the defined relations a number of sequent type calculi is constructed; their characteristic features are extended conditions for sequent closure and original forms for quantifier elimination.
PROBLEMS IN PROGRAMMING, 2019
Досліджено нові програмно-орієнтовані логічні формалізми-логіки часткових предикатів з операцією ... more Досліджено нові програмно-орієнтовані логічні формалізми-логіки часткових предикатів з операцією (композицією) предикатного доповненням, названі LC. Подібні операції використовуються в різних варіантах логік Флойда-Хоара з частковими перед-та після-умовами. В даній роботі вивчаються LC пропозиційного рівня-PLC. Описано пропозиційні композиційні алгебри та мови PLC, запропоновано та досліджено відношення неспростовнісного логічного наслідку за умов невизначеності. На цій основі для PLC однозначних предикатів побудовано числення секвенційного типу. Ключові слова: логіка, предикат, логічний наслідок, секвенційне числення.
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Papers by Mykola Nikitchenko