**INFORMATION ABOUT PROJECT,
SUPPORTED BY RUSSIAN SCIENCE FOUNDATION**

*The information is prepared on the basis of data from the information-analytical system RSF, informative part is represented in the author's edition. All rights belong to the authors, the use or reprinting of materials is permitted only with the prior consent of the authors. *

COMMON PART

Project Number17-11-01176

Project titleNew generation logic-probability instruments for artificial intelligence

Project LeadGoncharov Sergey

AffiliationSobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences,

Implementation period | 2017 - 2019 |

Research area 01 - MATHEMATICS, INFORMATICS, AND SYSTEM SCIENCES, 01-101 - Mathematical logic and foundations of mathematics

Keywordsmathematical logic, semantic programming, artificial intelligence, logic programming, big data, stream data, ontology, subject domain, logical inference, corporative control systems, distributed and network data

PROJECT CONTENT

Annotation

The project is aimed at
- advancing the theory and methodology of Semantic Programming, which is a programming paradigm proposed in 1980’s by acad. S.Goncharov, Yu. Ershov, and prof. D. Sviridenko, and further developed by the groups of prof. E.Vityaev (probabilistic approach) and A. Mantsivoda (logic-based approach);
- applying Semantic Programming to a variety of information management problems, which would benefit from the AI methodology, but require a significant improvement in scalability of the available AI methods and algorithms.
The principal features of Semantic Programming, which distinguish it from the known logic-based AI formalisms for specification and execution of computations (e.g., Prolog, Lisp, Refal, etc.) are the following:
1. the language used to define executable problem specifications in Semantic Programming relies on the language of E-formulas of first order predicate calculus, which contrasts with Prolog (based on Horn fomulas) and Lisp (based on lambda-expressions);
2. Semantic Programming is rather a logic modeling language, than a programming language in a traditional sense;
3. execution (or computation) in Semantic Programming does not mean logical inference, transaction, or expression transformation, but relies on model checking for specification formulas, with a model being a formal representation of a subject domain;
4. Semantic Programming provides tools based on bounded quantification to optimize specification execution.
These are the distinguishing features of Semantic Programming, which make it advantageous in solving problems involving a large number of logic relationships that are relatively simple units from the computational point of view (this is the case, e.g., in the context of Big Data).
On top of that, the probabilistic extension of Semantic Programming developed in the group of E. Vityaev has benefits in comparison with probabilistic logic programming:
5. it allows to discover maximally specific knowledge that can be used to make consistent predictions. Using maximally specific rules allows for obtaining a probabilistic extension of formal concepts and producing a classification of objects and knowledge of a subject domain of interest.
In this project, a new class of subject domain models (so called locally simple models) is studied, which has appeared in applied tasks related to process management in business and industry. This class of subject domain models is general and practical, as well as specific enough to allow for efficient tools that could solve problems of real-world complexity in real time. The experience of working with models of this kind evidences that the existing AI methods and tools are not efficient enough for solving information management problems in the mentioned areas. In the project, we propose a new approach coupling the formalism of Semantic Programming with probabilistic and statistical methods to address vague, imprecise, and suboptimal models, which often occur in practice. These methods have benefits when working with models having a large number of components, since they allow for avoiding logical inference, which can be disadvantageous in solving hard combinatorial problems. Probabilistic and statistical methods for model analysis are less precise, but at the same time appear to be cheaper than pure logic-based methods.
It is important to note that the research on methods that provide suboptimal solutions has become a recent trend, since it is known that optimal solutions are non-stable against even some minor noise, which can often occur in practice. At the same time, computing suboptimal solutions appears to be much cheaper, than computing precise ones.
As the practical outcome of coupling Semantic Programming with probabilistic methods, a software platform will be developed, which allows for making prototypes of locally simple models and performing their optimization. This platform could open the way to solving the following problems:
- developing automated business management systems capable of monitoring and controlling, as well as planning and predicting company operation;
- building cloud computing services including smart processing services for big and streaming data;
- developing smart call centers and chatbots, which are capable of communicating in natural language;
- building automated systems for bid and contract management having self-monitoring and conflict resolution functions;
- smart protection and processing of distributed and/or network data;
- developing logic specifications and knowledge bases using domain ontologies;
- developing methods of smart data analysis using domain ontologies.

Expected results

In order to address the information management problems mentioned in section 1.4 the first stage of the project is focused at developing theory and methods of a probabilistic dialect of the Semantic Programming language. The dialect is obtained as a combination of the following languages:
- a probabilistic statistical dialect of the Semantic Programming language developed in Novosibirsk in the group lead by E. Vityaev
- a logic-based dialect developed in Irkutsk in the group lead by A. Mantsivoda.
At the second stage it is planned to develop a formal description of a unified dialect with a denotational and operational semantics and a prototype solver for the obtained formalism.
The third stage of the project will be devoted to application of these tools in solving the above mentioned information management problems taking into account their properties and specifics. The main outcome of this work will be executable semantic specifications of these problems in terms of the developed unified dialect of Semantic Programming. The specifications will be focusing practical applications in tools for smart data processing.
Using Semantic Programming extended with probabilistic and statistical methods for description of locally simple management models will allow for making a significant advance in the area of complex business process management. These are the specifics of the proposed project that make the foreseen results not only scientifically, but also practically valuable. The essence of the locally simple enterprise modeling approach is to avoid hard coding business logic, but instead represent it using logic models. This gives a number of important benefits:
- modeling allows for a smooth and faster system implementation;
- models are much more flexible and scalable than software modules, they are more elastic to enterprise evolution;
- systems based on models are easier to explain, since they employ modeling of work places using concepts that are familiar to employees;
- modeling allows for solving big data related problems in a number of important situations by converting data flows into semantic structures that enrich the corresponding locally simple models;
- using modeling allows for significantly reducing software and implementation costs, which makes enterprise management systems more accessible to companies;
- modeling opens the way to making routine management tasks fully automated by using logic-based and probabilistic tools.
Thus, a probabilistic extension of Semantic Programming is capable of providing tools to describe locally simple models at an enterprise level with hundreds of millions of transactions per year. This is the scale of a big geographically distributed retailer, an industry holding, a transport company, or mobile network operator.

REPORTS

Annotation of the results obtained in 2019

In 2019, project research was conducted in three areas - methodological, theoretical and applied.
In 2019, the methodological research of the task-oriented approach to the problems of artificial intelligence (AI) and cognitive sciences continued. The results of the research included two articles, one of which was devoted to artificial intelligence and the other to the application of the task-oriented approach to cognitive sciences, where the concept of purpose is the analogue of the task.
One of the important results of methodological research on the application of the task-oriented approach to the AI was the description of the content, composition and architecture of the semantic model of the subject area to which the problem is related. If at the solution of a task it is possible to manage only a knowledge component of semantic model, such a problem is called a direct one and its solution in AI is usually engaged in symbolic AI. If, however, only the second component of the semantic model - precedents (Big data) - is used in solving the problem, then such problems are called reverse and their solution is the subject of attention of machine learning. However, the most interesting and at the same time the most complex and large-scale class of tasks is the class of hybrid tasks, for which both knowledge and precedents are necessary. It has been shown that semantic modeling makes it possible to solve such hybrid tasks very successfully, since the formalism of semantic modeling allows us to adequately represent the peculiarities of subject areas, formulating statements about both syntactic and semantic properties of these areas, and thus representing a single language for the construction, validation and verification of semantic formal models of these areas. As an example of a successful solution of a complex hybrid problem, we can point out the construction of an effective hybrid system of adaptive control of modular robots carried out within the framework of the project.
Work continued on methodological aspects of creating complex information systems that demonstrate the advantage of semantic modeling over traditional programming. It was shown that the replacement of programming with semantic modeling has a breakthrough qualitative effect in many areas. These results were reflected in an article published in the Bulletin of Irkutsk State University.
Theoretical studies undertaken earlier in the project have shown that logical modeling of subject areas can often be limited to so-called ∆0 formulas and ∆0termas, in which only limited quantization is allowed. This limitation allows us to focus only on effective calculations, i.e. on calculations of a given, for example, polynomial complexity, which makes it possible, in contrast to the axiomatic approach, to carry out an effective synthesis of solutions to problems of predetermined complexity. In the course of theoretical work on the project in 2019, the thermal expansion of the ∆0-formula language was studied by constructions simulating recursion on the list, iteration limited by the constant, and search on the lists. The exact estimation of the problem of truthfulness in the given list superstructure and the problem of feasibility in some list superstructure for ∆0 formulas with the listed types of terms was obtained. It is established that the expansion of the ∆0-formula language with recursive or iterative terms covers all polynomial functions. It follows that any restriction on the quantum prefix of formulas, which guarantees polynomial verification of the validity of the ∆0-formulae of the base language, results in a P-fullness of the corresponding thermal expansion of the semantic modeling language.
The most important concept in cognitive sciences is anticipation and prediction. In the AI, predictions are made by inductively using the I-S output (Inductive-Statistical inference). However, it is known that predictions obtained by the I-S conclusion can lead to contradictions. In order to overcome this contradiction in the design works it was formally defined the requirement of maximum specificity and it was proved that the I-S conclusion of the prediction according to the most specific rules does not lead to contradiction. This allowed us to determine the most specific rules, the detection of which gives a system of rules that predict without contradictions.
It should be noted that in cognitive sciences the learning process is often considered as a process of discovery of causal relations. Previously, in the course of project studies, a formal neuron model satisfying the Hebbian rule was determined, which detects cause-effect relationships in the form of maximally specific rules. Assuming that the brain in consciousness makes all possible conclusions on cause-effect relations, the model of consciousness corresponding to this assumption was described and this model was compared with the works of P.K.Anokhin, P.V.Simonov, G.Tononi and other scientists.
As to practical orientation of theoretical design works here, first of all, it is necessary to mention works on automation of the enterprises. It has turned out that for work with an unlimited number of documents of language ∆0-formulae is not enough and it is necessary to go beyond the limits of the given language, i.e. consideration of already sigma-formulae with unlimited quantaires of existence on the lists presenting documents. In this connection, a question arose about the algorithmic solvability of the problems of verification of document models. Besides, there appeared a problem of recognition of transaction completeness over documents. Within the framework of the project it was shown that, in general, the problem of verification of document models in the conditions of unlimited creation of documents is algorithmically unsolvable. The conditions were formulated for the type of theory describing the document model, sufficient to effectively solve the problem of document model compatibility and completeness of the transactions described in it. The concept of an oracle in document models is also formulated. The approach to the solution of the planning problem within the framework of formalization of document models by means of semantic modeling is proposed. Proceeding from the found conditions on the form of the theories of document models, the concept of locally simple document model as the theories with the limited set of expressive language constructions and solvable properties of compatibility and completeness of transactions is formulated. At the same time, it was shown that if the transaction description language allows the creation of new documents in loops based on samples of previously created documents, then transactions can generate an exponential number of documents (from a given number of n) for any height of the exhibitor. The same number of calculation steps is required to build the result of transaction execution. If creation of documents in loops is prohibited, the result of transaction execution over the document model can be calculated for a polynomial number of steps. These results are the content of a separate article adopted for printing in 2019 (in the Bulletin of Irkutsk State University).
As part of the study of the process of formalization of the document approach through the concept of partially computed finite type functionalities, the study of classifications of postings of document models as computed numbers of families of functionalities over a given basic model was continued. By results of the research the article was published.
As part of the design work carried out in 2019, the problem of combining ontological descriptions of subject areas formulated in the family of logic DL-Lite, which have many convenient properties of propositional logic and at the same time allow the limited use of binary predicates was considered. The results obtained here provide the basis for building mechanisms for combining logical descriptions of subject areas, which guarantee the absence of the effect of complication.
Within the framework of the project the work on technological aspects of creation of IT-systems by methods of semantic modeling was continued. The technology of a stationary point that has allowed to use effectively static logic models for the description of dynamically changed worlds has been developed. Now this technology is applied in a number of projects of industrial level: system of budgeting of the large enterprise, system of business analysis of sales of the network retailer, system of management of human resources of the enterprise and others. Practice has shown that at application of semantic modeling it is reached, at least, fivefold increase in labour productivity, both in the course of working out, and support, and modernization of information systems, with corresponding economy of financial, labour and time resources.
Within the limits of the project the cloud platform of management of document models and construction of semantic web-services bSystem has also been developed. The approach to construction of business processes on the basis of semantic document models has been developed. The natural formalization of business processes through sequence of changes of documents is offered. It is noticed that the popular concept of the smart contract is a special case of business process in such formulation. The results are published in the Bulletin of Irkutsk State University.
It is necessary to notice that scalability of semantic models is provided by platform bSystem both at semantic level, and at the bottom level, allowing not only to develop and maintain scalable semantic models of the big sizes, but also to build on their basis various web services and API for remote interaction with other services. A special technology of dynamic compilation of Libretto-programs was developed to provide interaction between model and software components. For each semantic model, the Libretto software library is automatically generated in real time, through which the model is accessed from the Libretto environment. In bSystem one more component is integrated - the module of a logic-probabilistic conclusion, allowing to solve within the limits of a platform of problems of an artificial intelligence. Within bSystem the concept of clever contracts which is under construction as system of documents within the limits of semantic model is realised also. For maintenance of the decentralised mechanisms of trust the concept of the virtual document operated bSystem as a usual element of documentary model, keeping physically the basic parametres of the virtual document in external blockchain is realised. It opens essentially new possibilities for advancement of semantic clever contracts in the conventional economic environment. In conclusion, we would like to note that several semantic models of the industrial level (tens and hundreds of millions of ∆0 formulas) are currently being developed on the basis of the bSystem.
Another direction of design practical works is connected with robotics. Existing approaches to adaptive control of hyper-surplus and modular systems are most often based on the use of Reinforcement Learning and evolutionary approaches, which are limited by the impossibility of learning to solve multi-level problems, weak scalability with respect to increasing the number of degrees of freedom, the impossibility of learning in real life mode, the need to create a separate control system for each configuration of the robot, etc. These limitations strongly inhibit the practical use of modular and reconfigurable robots that require universal control systems that do not depend on a particular configuration. Within the framework of the present project the task was solved - using methods of semantic modeling and probabilistic forecasting to develop a universal control system for modular hyper-surplus systems, capable of independently finding ways to control robots with arbitrary design from a given class, as well as able to learn and adapt. At the same time, the experimental part of the work should have included computer experiments on teaching the ways of moving virtual robot models in a software environment that simulates the laws of real-world mechanics. At its decision the way of the description of a design of robots in the form of a tree of the elements describing a site of modules and connection between them has been offered, and the problem of training of a control system has been reduced to a problem of detection of laws on the heterogeneous data. Formalization of sensor-motor information of the system and information about the robot design by means of semantic modeling language was proposed. On the basis of the semantic probability conclusion the method of detection of effective control rules of the set kind from files of the statistical data on interaction of system with the world around has been developed. Experiments were carried out to teach virtual robot models how to move forward. Experiments were conducted in a special software environment. The results confirmed the applicability and high efficiency of the proposed approach and were published in several works.
Translated with www.DeepL.com/Translator (free version)

Publications

**1.** *Vityaev E.E.* **Consciousness as a Brain Complex Reflection of the Outer World Causal Relationships** Advances in Intelligent Systems and Computing 10th Annual International Conference on Biologically Inspired Cognitive Architectures, BICA 2019; Seattle; United States; 15 August 2019 - 18 August 2019, Volume 948, Pages 556-561 (year - 2020).

**2.** *Vityaev E.E.* **Consciousness as a logically consistent and prognostic model of reality** Cognitive Systems Research, 59, 231–246 (year - 2020).

**3.** *Vityaev E.E., Odintsov S.P.* **How to predict consistently?** Studies in Computational Intelligence, Volume 796, Pages 35-41 (year - 2019).

**4.** *Mantsivoda A.V., Ponomaryov D.K.* **Towards Semantic Document Modelling of Business Processes** The Bulletin of Irkutsk State University. Series “Mathematics”, v.29, p. 52-67. (year - 2019).

**5.** *Mantsivoda A.V., Ponomaryov D.K.* **On Termination of Transactions over Semantic Document Models** The Bulletin of Irkutsk State University. Series “Mathematics”, - (year - 2019).

**6.** *Demin A.V.* **Адаптивное управление роботами с произвольно заданной модульной конструкцией** Известия Иркутского государственного университета. Серия «Математика», Т. 29. С. 10-21. (year - 2019).

**7.** *Goncharov S.S., Sviridenko D.I.* **Logical Language of Description of Polynomial Computing** Doklady Mathematics, Dokl. Math. (2019) 99: 121 (year - 2019).

**8.** *Ospichev S.S.* **Friedberg numberings of families of partial computable functionals** Siberian Electronic Mathematical Reports, vol 16, p 331-339 (year - 2019).

**9.** *Vityaev E.E., Goncharov S.S., Sviridenko D.I.* **On the task approach to artificial intelligence** Siberian Journal of Philosophy, 2019. V. 17, No. 4. P. (year - 2019).

**10.** *Demin A.V.* **Adaptive locomotion control system for robots with arbitrarily modular design** Procedia Computer Science, - (year - 2019).

**11.** *Kazakov I.A., Kustova I.A., Mantsivoda A.V.* **Документное моделирование: методология и приложения** Известия Иркутского государственного университета. Серия Математика, - (year - 2020).

**12.** *Goncharov S.S., Sviridenko D.I.* **Проблемы цифровизации и семантическое моделирование** Материалы XII Мультиконференции по проблемам управления (МКПУ-2019), Том 1, стр.16-19 (year - 2019).

**13.** *Vityaev E.E., Goncharov S.S., Sviridenko D.I.* **О задачном подходе в искусственном интеллекте и когнитивных науках** Сибирский философский журнал, Том. 18, №2, стр.5-29 (year - 2020).

**14.** *Goncharov, S.S., Sviridenko, D.I., Vityaev, E.E.* **Task approach to artificial intelligence** CEUR Workshop Proceedings, Volume 2642 (year - 2020).

**15.** *S. GONCHAROV, S. OSPICHEV, D. PONOMARYOV, D. SVIRIDENKO* **THE EXPRESSIVENESS OF LOOPING TERMS IN THE SEMANTIC PROGRAMMING** СИБИРСКИЕ ЭЛЕКТРОННЫЕ МАТЕМАТИЧЕСКИЕ ИЗВЕСТИЯ, Том 17, стр. 380–394 (year - 2020).

**16.** *Goncharov, S., Sviridenko, D.* **Semantic Modeling and Hybrid Models** SIBIRCON 2019 - International Multi-Conference on Engineering, Computer and Information Sciences, Номер статьи 8958196, Pages 987-990 (year - 2019).

**17.** *S. S. Goncharov & D. I. Sviridenko* **Recursive Terms in Semantic Programming** Siberian Mathematical Journal, v. 59, pages1014–1023 (year - ).

Annotation of the results obtained in 2017

One of the most notable trends associated with the rapidly advancing era of digitalization is a significant strengthening of the role of semantic methods of controlling meanings and knowledge in solving problems, which inevitably leads to an increase the role of logical-mathematical and probability methods working with semantics. Semantic programming, based on the use of logic-probabilistic modeling tools, is an original approach to solving problems for a wide range of important subject areas. In this project we are talking about subject areas that can be represented in the form of locally simple models (LPM), which allows us to successfully solve very complex tasks in a variety of areas, and above all, in the management of enterprises, organizations, and authorities. The most important feature of locally simple models is their ability to replace programming with modeling, which gives colossal advantages: the costs of system development and support are dramatically reduced; modeling, unlike programming, preserves the explicit semantics of models, leaving work opportunities for artificial intelligence and robots. In addition, such models are much more understandable to people than programs.
The reporting year was mainly devoted to the solution of methodological and theoretical problems, but in parallel, practical tasks were also solved.
The main methodological results obtained in the reporting year relate to the development of a task approach:
1. The ontology of the subject domain is proposed to be implemented in the form of a multi-sorted model equipped with a finite-hereditary lists superstructure and a finite set of formulas-definitions and formulas-knowledge that are true on this model;
2. The formulation of the task and the criterion for its solution is given by the formula A, such that A is true, if and only if the original problem is solved. Effective calculation of the truth of the formula A and is the criterion for solving the task.
3. By virtue of the requirement of computational efficiency, it is proposed to limit the formula representation of LPM and tasks to Δ0-formulas for solving the problem.
In view of the important role of the concept of "computational complexity," research was initiated in the framework of the project on the algorithmic complexity of realizing semantic programs. A study was carried out of the complexity of Δ0-formulas, including the complexity of Δ0-formulas of a language extended by additional thermal functions, such as, for example, conditional terms. It was shown that the extension of the language of Δ0-formulas by conditional terms is conservative and that the use of conditional terms does not violate the polynomial complexity of the computations.
The methodology of problem solving developed in the project was successfully applied to the Theory of Inventive Problem Solving (TRIZ), which allowed to interpret and develop this theory, as the Theory of Solving Innovative Tasks, including business tasks.
Approbation of the method of semantic modeling on the basis of LPM was carried out at two large classes of applied problems. Work is underway to prepare for the implementation of the Digital Baikal project.
During the reporting period, the LPM architecture was actively investigated. The basic types of its submodels were identified and described: the locale, the report, the competence and the oracle. The LPM itself is built with the help of a model designer from the submodels of the listed types, implemented in the framework of the bSystem web service, accessible via the Internet. The process of model management occurs within the public or corporate cloud environment, formed by the web service bSystem.
It is shown that locally simple simulation is effectively realized through document models with finite submodel coatings. An example of document models using for solving a management problem of real complexity is described. Mechanisms for storing document models were developed. The architecture of the two-level storage with graph top level and relational lower level developed. Mechanisms based on the concept of optimistic parallelism were developed.
In connection with the importance of practical aspects, we analyzed:
• the problem of choosing concepts and semantics with clear meanings to the user;
• сompatibility problem of domain ontologies.
Following the original approach to the semantic combination of ontologies, for an extensive class of descriptive logics, an algorithmic classification of the logical sequence problem from semantically related ontologies was obtained. It is shown that acyclic semantic combination leads to an increase in the complexity of the logical sequence problem. The results of the research provide the basis for implementing new practical methods of combining ontologies.
A method is proposed for calculating explicit definitions of concepts with respect to ontologies in the descriptive logic EL based on the directional deduction calculus. It is shown that, in the logic of EL, the notion of an ontology in the worst case can have a double exponential number of shortest and pairwise incomparable definitions, each of which has an exponential length (on the size of the ontology). An algorithm for computing explicit definitions of concepts is developed and implemented.
The generation of ideas for the solution of the task must be accompanied by a forecast (prediction) of the possibility of solving it. To this end, methods of probabilistic forecasting were developed as a variant of the inductive-statistical (I-S) prediction model. Problems were solved: (1) statistical ambiguity, when from the inductively derived knowledge a contradictory prediction is obtained and (2) the synthesis of logic and probability, when estimates of the probability of predictions, which follow the implementation of the logical inference, drop sharply and often reach zero.
To solve the first problem, Karl Hempel, at one time, suggested using only the most specific rules in I-S-inference and gave a fairly precise, but informal definition of such rules. After it, a formal definition of the most specific rules was not proposed. The project gives a formal definition of maximally specific rules and proves that the application of a logical inference to a consistent set of maximal specific rules gives a consistent set of consequences. Thus, the problem (1) of statistical ambiguity is solved and the consistency of the predictions in I-S- inference for maximum specific rules is proved. To detect the most specific rules, a special semantic probability inference was determined, which also solves the problem (2). Within the framework of the project, it was proved that the predictions obtained by the I-S- inference, using the most specific rules, approximate the estimates of the predictions obtained after the implementation of the logical one.
Despite the high effectiveness of Deep Learning methods, they remain a "thing in itself", a "black box", decisions of which can not be trusted. This is critical for such areas as medicine, financial investments, military applications and others, where the price of the error is too high. The project proposes an alternative, logical-probabilistic method of in-depth training, capable of explaining its decisions. This is a method of hierarchical clustering, based on the original logical-probabilistic generalization of formal concepts.
Based on the semantic probabilistic inference as a learning process, a control system for modular robots with a large number of degrees of freedom has been developed. Experimental studies have shown that the proposed approach can be used to control complex modular robots that have many degrees of freedom.

Publications

**1.** *Kazakov I.A., Kustova I.A., Lasebnikova E.N., Mantsivoda A.V.* **Построение локально-простых моделей: методология и практика** Известия Иркутского государственного университета. Серия "Математика", Том 22. C.71-89 (year - 2017).

**2.** *Sviridenko D.I. , Sibiryakov V.G.* **ТРИЗ- теория решения инновационных задач: часть 2. Как решать инновационные задачи: разработка концепции инновации.** Сибирская финансовая школа. Инновации, т. 123, № 4, с 21-37 (year - 2017).

**3.** *Vityaev E.E.* **СЕМАНТИЧЕСКИЙ ВЕРОЯТНОСТНЫЙ ВЫВОД ПРЕДСКАЗАНИЙ** Известия Иркутского государственного университета. Серия "Математика", Т. 21. С. 33—50 (year - 2017).

**4.** *Sviridenko D.I. , Sibiryakov V.G.* **ТРИЗ и семантическое моделирование** Труды IX международной конференции «ТРИЗ. Практика применения и развитие методических инструментов 10-11 ноября 2017 г., т.2 стр.139-150. (year - 2017).

**5.** *Goncharov S.S.* **Условные термы в семантическом программировании** Сибирский математический журнал, т. 58, №. 5, с. 1026–1034, 2017 (year - 2017).

**6.** *Malykh A.A., Mantsivoda A.V.* **Документное моделирование** Известия Иркутского государственного университета. Серия "Математика", Т. 21. С. 89—107 (year - 2017).

**7.** *Vityaev E.E., Odintsov S.P.* **How to predict consistently?** Oral communications, 9th European Symposium on Computational Intelligence and Mathematics, Faro, Portugal, October 4th-7th, 2017, - (year - 2017).

**8.** *Demin A.V., Vityaev E.E.* **Adaptive Control of Modular Robots** A.V. Samsonovich and V.V. Klimov (eds.), Biologically Inspired Cognitive Architectures (BICA) for Young Scientists, Advances in Intelligent Systems and Computing 636, - (year - 2018).

**9.** *Vityaev E.E., Martynovich V.V.* **Прозрачное глубокое обучение на основе вероятностных формальных понятий в задаче обработки естественного языка** Известия Иркутского государственного университета. Серия "Математика", Том 22. C.31-49 (year - 2017).

**10.** *Sviridenko D.I. , Sibiryakov V.G.* **ТРИЗ- теория решения инновационных задач: часть 1. Что такое инновационная задача.** Сибирская финансовая школа. Менеджмент и инновации, Т.122, № 3, с. 26-35 (year - 2017).

Annotation of the results obtained in 2018

Studies on semantic programming in the reporting year were both theoretical and applied.
A comparative analysis of instrumental and language means of two close programming concepts - declarative and semantic. A significant practical advantage of the model-theoretic model of computability, which forms the basis of semantic programming, over the axiomatic model on which declarative programming is based, was shown. As one of these advantages, the ability to fully preserve the original semantics of the problem was noted, which allows us to formulate the concept of “explanatory” artificial intelligence (Explanable Artificial Intelligence). Another important advantage of semantic modeling is the controlled (from the point of view of computational complexity) possibility of significantly enhancing the expressive properties of a language by using various additional schemes for defining terms, oracles and special operators that “prompt” the calculator the most optimal way to execute semantic programs. An important advantage of semantic programming is also the ability to create hybrid models that combine models and algorithms of different nature into a single whole, which allows, for example, instead of the traditional machine (deep) learning, to offer a fundamentally different method based on a combination of mathematical-statistical and logical approaches. It is clear that further development of the concept of semantic hybrid modeling will require the solution of a number of new problems, among which we emphasize the problem of semantic protocols, which allow us to build communication relationships between different models in a uniform way, and the problem of verifying “correctness” (operability, correctness, optimality, etc. ) hybrid models. According to the research published one article: Goncharov S.S., Sviridenko D.I. Semantic modeling and artificial intelligence // Siberian philosophical journal, 2018, volume 16, №4, p.5-29, and one submitted to print: Goncharov S.S., Sviridenko D.I. Semantic modeling and hybrid models//2018 Siberian Symposium on Data Science and Engineering (SSDSE), Novosibirsk, Russia, 2018, ISBN: 978-1-7281-0399-0
It is shown that the extension of ∆0-formulas over structures with hereditarily finite lists of conditional and recursive definition of terms is a conservative enrichment, and new terms are delta-definable in the main language. The complexity of the problem of the truth of ∆0-formulas for the cases of a limited quantifier prefix and an extension of the class of thermal functions, obtained, in particular, by adding conditional and recursive terms, is investigated. It is proved that the complexity of verifying the truth is polynomial in the case when the prefix contains k quantifiers for fixed k. If the prefix contains k alternations of quantifiers, then the problem is complete with respect to the level k of the polynomial hierarchy. Without limiting the quantifier prefix, the problem is PSPACE-complete. The results obtained draw a parallel between the truth problem of ∆0-formulas with conditional terms and a similar well-known problem for quantified Boolean formulas and show the limits of efficiency in terms of the syntax of formulas. According to the results, two journal articles were published (Goncharov S. S., Sviridenko D. I. Recursive terms in semantic programming // Vol. 59 (2018), Number 6, p. 1279–1290; S. Ospichev and D. Ponomarev. On The Complexity of Formulas in Semantic Programming. Siberian Electronic Mathematical Reports. 15: 987-995, 2018) and one accepted for publication (Goncharov S.S., Sviridenko D.I. Logical language for the description of polynomial computability // Reports of the Russian Academy of Sciences, 2018) .
The dialect of the semantic modeling language is defined, the expressiveness of which corresponds to the document models. It is shown that the key problems of verifying document models are reduced to verifying the logical following of formulas of a certain type from the theory describing the document model. According to the results of the work a journal article was prepared (A. Mantsivoda, D. Ponomarev. A Formalization of Document Models with Semantic Modelling. Известия Иркутского государственного университета. Серия Математика, 2019).
The algorithmic classification of dialects of the semantic modeling language, determined by syntactic restrictions on the type of quantifier prefix of formulas, and the algorithmic classification of the complexity of the logical following problem from semantically related terminological descriptions, formulated in the family of descriptive logics DL-Lite, are obtained. A method for calculating definitions of concepts in terminological descriptions is proposed. The complexity of the problem of logical following from semantically related descriptions in the family of descriptive logics DL-Lite is investigated. A method has been proposed for finding definitions of terms in the signature specified by the user. The method is implemented as an extension (plug-in) for the Protégé ontology editor (https://protege.stanford.edu), using the ELK automatic proof machine for obtaining evidence and the ELK explanation service, which allows the user to see the explanation. According to the results of the work, an article was prepared in the conference proceedings: Denis Ponomaryov and Stepan Yakovenko. DeFind: A Protégé Plugin for Computing Concept Definitions in EL Ontologies. Proceedings JIST2018, 8th Joint International Semantic Web Conference, Awaji City, Hyogo, Japan, Springer, LNCS 11341, pp. 235-243.
The semantic approach was applied to the cognitive sciences, where the concept of a goal is an analogue of the concept of a task. Taken in E.E. Vityaev, A.V. Demin. Cognitive architecture based on the functional systems theory // Procedia Computer Science. The 2019 analysis of the brain's purposeful activity, based on the Theory of Functional Systems (TFS), made it possible to formalize the same type of architecture of the central mechanisms of the functional systems that provide purposeful behavioral acts. Formalization is based on semantic probabilistic inference. As a result, a hybrid system of adaptive control was obtained, which, on the one hand, precisely formalizes TFS as a system for solving brain needs-based tasks, and, on the other hand, implements the idea of hybrid semantic modeling.
The effectiveness of the above-mentioned adaptive system was confirmed in experiments on intelligent self-learning robots interacting with the environment and learning from their experiences. The task of developing a universal control system for modular hyper-redundant systems was solved using the methods of semantic programming and probabilistic forecasting for training and adaptation. At the same time, the task of learning the management system was reduced to the task of finding patterns in the array of statistical data on the interaction of the system with the environment. On the basis of semantic probabilistic inference, a method was developed for detecting effective control rules of a given type from arrays of statistical data on the interaction of a system with the surrounding world. To test the applicability of the proposed approach, experimental studies have been conducted to teach simple modular robots how to move forward. The results obtained confirmed the applicability and effectiveness of the proposed approach. The research results published in the works: Demin A.V. Vityaev E.E. Adaptive Control of Modular Robots // Biologically Inspired Cognitive Architects (BICA) for Young Scientists. - Springer, 2018. - pp. 204-212; Demin A.V., Vityaev E.E. Adaptive control of multiped robot // Procedures Computer Science, 2019 (accepted for printing).
Research continued on the task of clustering within the framework of the Formal Concept Analysis (AFP) theory, focused on finding formal concepts that combine similar attributes and objects, as well as building a hierarchy of formal concepts in the form of a conceptual grid, its subsequent processing and visualization. Since the existing methods for constructing a lattice of concepts on a noisy data context turn out to be unproductive, an original semantic method was developed to form an initial lattice of concepts on noisy data using semantic probabilistic inference, which generalizes the concept of implication by introducing a probabilistic measure and a derivability operator in formal contexts. A special set of implications is determined for which a probabilistic generalization of formal concepts is introduced, and an algorithm for direct search for generalized formal concepts is proposed. The results are published in an article by E.E. Vityaev, V.V. Martynovich. Probabilistic formal concepts on noisy data // Siberian Journal of Pure and Applied Mathematics. Vol. 17, No. 4, 2017, pp. 28–38.
As part of the project, work continued on improving the methodology and technology of developing IT systems. Within the bSystem platform, the technology for constructing executable semantic models was developed and implemented as tools for building industrial-level information systems, given that the models are open systems subject to external forces, which are modeled using oracles. In order to reflect these moments in the documentary modeling, the concept of the life cycle of documentary models was developed and formalized, based on the mechanism of reaching the fixed points by the model in order to control the processing of erratic or unfair oracles' behavior (A. Mantsivoda, D. Ponomarev. A Formalization of Document Models with Semantic Modelling. Известия Иркутского государственного университета. Серия Математика, 2019). Currently, the created technology has been applied in a number of industrial-level projects. The practice of its use has shown that with its help it is possible to achieve at least a fivefold increase in labor productivity with corresponding savings in financial, labor and time resources.
In the framework of applied research, the analysis of the concept of semantic smart contract was continued, providing fundamentally new opportunities for designers and users of contractual relationships. Note that the concept of semantic smart contracts separates contracts from a centralized or distributed registry used in their execution — there may be several such registries and the choice of the necessary should be determined by the conditions and properties of the contract itself. An analysis was made of the use of smart contracts in other technologies. The reasons for the weak spread of technology of smart contracts based on programming languages such as Solidity are identified. The analysis made it possible to develop an original methodology and technology for using document models as one of the foundations for managing semantic smart contracts. It was proposed to represent the semantic smart contract as a logical document within the framework of the document model, which allows considering the semantic contract as a structured declarative description, where decentralized trust mechanisms are implemented through the integration of document models with the blockchain system. At the same time, the type of blockchain system used in conjunction with the document models is a technology parameter and is a subject of choice by the contractor community. Within the framework of the described methodology, a working prototype of the semantic contract management system was developed in the form of a cloud web service, on the basis of which a number of experiments were conducted necessary for further clarification and development of the methodology and technology of semantic contracts.
Methodological foundations of creating a new generation of electronic wallets - semantic smart wallets (Sviridenko DI, Semantic Smart Wallets // 2018 Siberian Symposium on Data Science and Engineering (SSDSE), Novosibirsk, Russia, 2018, ISBN: 978-1-7281-0399 -0 (in print)), considered as a special version of semantic smart contracts concluded by the owner of the purses with themselves. The main advantage of this approach is the ability of the potential wallet owner, using simple and clear semantic modeling tools, to either create a smart wallet with the service he needs, or to choose the most suitable one from a number of already existing wallet templates.
The research results are reflected in the following information resources on the Internet:
https://expert.ru/siberia/2018/13/tsifrovizatsiya-iznachalnaya/
https://expert.ru/dossier/author/dmitrij-sviridenko/
https://kirik.io
https://www.uni-log.org/start6.html

Publications

**1.** *Goncharov S.S., Sviridenko D.I.* **Рекурсивные термы в семантическом программировании** Сибирский математический журнал, № 6, т. 59, с. 1279-1290 (year - 2018).

**2.** *Vityaev E.E., Demin A.V.* **Cognitive architecture based on the functional systems theory** Procedia Computer Science, Springer, Procedia Computer Science 145C (2018) pp. 623-628 (year - 2018).

**3.** *Goncharov S.S., Sviridenko D.I.* **Семантическое моделирование и искусственный интеллект** Сибирский философский журнал, 2018, том 16, №4, с.5-29 (year - 2018).

**4.** *Ospichev S., Ponomarev D.* **On the complexity of formulas in semantic programming** Siberian Electronic Mathematical Reports, Том 15, стр. 987–995 (2018) (year - 2018).

**5.** *Demin A.V., Vityaev E.E.* **Adaptive Control of Modular Robots** Samsonovich A., Klimov V. (eds) Biologically Inspired Cognitive Architectures (BICA) for Young Scientists. BICA 2017. Advances in Intelligent Systems and Computing, Advances in Intelligent Systems and Computing v. 636, Springer, 2018, pp. 204-212 (year - 2018).

**6.** *Vityaev, E., Odintsov, S.* **How to predict consistently?** Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, 2019, vol 796, pp 35-41 (year - 2019).

**7.** *Vityaev E.E., Martinovich V.V.* **Вероятностные формальные понятия на зашумленных данных** Сибирский журнал чистой и прикладной математки, 2017,том 17,выпуск 4,страницы 28–38 (year - 2017).

**8.** *Mantsivoda A., Ponomarev D.* **A Formalization of Document Models with Semantic Modelling** Известия Иркутского государственного университета. Серия Математика, - (year - 2019).

**9.** *Demin A.V., Vityaev E.E.* **Adaptive control of multiped robot** Procedia Computer Science, Springer, Procedia Computer Science 145C (2018) pp. 629-634 (year - 2018).

**10.** *Goncharov S.S., Sviridenko D.I* **Semantic modeling and hybrid models** 2018 Siberian Symposium on Data Science and Engineering (SSDSE), - (year - 2018).

**11.** *Sviridenko D.I* **Semantic Smart Wallets** 2018 Siberian Symposium on Data Science and Engineering (SSDSE), - (year - 2018).

**12.** *Ponomaryov D.,Yakovenko S.* **DeFind: A Protégé Plugin for Computing Concept Definitions in EL Ontologies** Springer - Lecture Notes in Computer Science, Proceedings JIST2018, 8th Joint International Semantic Web Conference, Awaji City, Hyogo, Japan, Springer, LNCS 11341, pp. 235-243 (year - 2018).

**13.** *-* **Доклад: Гончаров С.С. "О создании в Новосибирске Международного математического центра (ММЦ)."** Объединенный Ученый Совет. 06.11.2018. Доклад: Гончаров С.С «О создании на базе ИМ СО РАН Международного математического центра». Общее Собрание СО РАН. 07.11.2018, http://www.sbras.ru/ru/news/41719 (year - ).

**14.** *-* **Академик Юрий Ершов: Цифровой экономике без математиков не обойтись.** Новости сибирской науки, http://www.sib-science.info/ru/institutes/ekonomike-14082018 (year - ).

**15.** *-* **Об истоках цифровой экономики, о том, как давно она началась, каких специалистов требует и где делать центры компетенций, журнал «Эксперт-Сибирь» поговорил с академиком РАН, директором Института математики им С.Л. Соболева СО РАН Сергеем Гончаровым** Эксперт online совместно с журналом "Русский репортер". Экономика., https://expert.ru/siberia/2018/13/tsifrovizatsiya-iznachalnaya/ (year - ).

**16.** *-* **Дмитрий Свириденко. Чтобы умными стали контракты** Эксперт online совместно с журналом "Русский репортер". Экономика., Москва, 09.12.2018 (year - ).

**17.** *Goncharov S.S., Sviridenko D.I.* **Логический язык описания полиномиальной вычислимости** Доклады РАН, математика, - (year - 2019).