|
Article information
2020 , Volume 25, ¹ 3, p.142-151
Khabarov V.I.
Logical aspects of experimental design and analysis
Purpose. The purpose of this work is to formalize the tasks of active object identification based on the apparatus of model theory — a modern section of mathematical logic. Model theory allows putting the subject “planning and analysis of an experiment” in the context of semantic analysis. Semantic analysis is understood as establishing a correspondence between the world and its formal representation. From this point of view, the concept of the object under study is expressed in some applied theory, which allows applying formal methods of model theory to it. Methods. It is assumed that the model is derived for this theory as an interpretation process, in which the key role is assigned to the experimenter. As a research method, it is proposed to use commutative diagrams that reflect the process of interpretation and extension of communication diagrams for the so-called equipped theories of planning and analysis of experiments. Results. The properties of the proposed models are proved and examples for planning a regression experiment are presented as an illustration. It is proved that for linear models it is possible to construct a finitely axiomatization capable theory. Findings, originality. The obtained results can be used in the design of architectures for an intelligent system in experimental research, building an experiment ontology and creation of knowledge bases. These studies will allow using logical programming to implement images of the presented commutative diagrams for equipped theories as applied systems for planning and interpreting the experiment
[full text] [link to elibrary.ru]
Keywords: active identification, experimental design, model theory
doi: 10.25743/ICT.2020.25.3.015
Author(s):
Khabarov Valeriy Ivanovich
Dr. , Professor
Position: Professor
Office: Novosibirsk State Technical University
Address: 630087, Russia, Novosibirsk, Nemirovich-Danchenko St., 136
E-mail: Khabarov51@mail.ru
References:
1. Denisov V.I. Matematicheskoe obespechenie sistem EVM-eksperimentator (regressionnyy i dispersionnyy analizy) [Mathematical support of computer-experimenter system (analysis of regression and variance)]. Moscow: Nauka; 1977: 251. (In Russ.)
2. H’ajek, P., Havr’anek T. Mechanising hypothesis formation: Mathematical foundations for a generaltheory. Berlin, Heidelberg: Springer; 1978: 398.
3. Nalimov V.V. Teoriya eksperimenta [Theory of experiment]. Moscow: Nauka; 1971: 208. (In Russ.)
4. Keisler H.J., Chang C.C. Model theory. Amsterdam: North-Holland Publ. Company; 2012: 651.
5. Barwise J. Handbook of mathematical logic. North-Holland Publ. Company; 1977: 1153.
6. Thayse A., Gribomont P. Approche logique de l’intelligence artificielle. Paris: HERMES SciencePubl.; 2000: 393.
7. Chechkin A.V. Matematicheskaya informatika [Mathematical Informatics]. Moscow: Nauka; 1991: 416. (In Russ.)
8. De Groot M.H. Optimal Statistical Decisions. New York: McGraw-Hill Company; 1970: 489.
9. Seber G.A. Linear Regression Analysis. New York: John Wiley and Sons; 2003: 582.
10. Fedorov V.V. Teoriya optimal’nogo eksperiment [Theory of optimal experiment]. Moscow: Nauka;1971: 313. (In Russ.)
11. Fedorov V., Khabarov V. Duality of optimal design for model discrimination and parameter estimation. Biometrika. 1986; (73):183–190.
12. Khabarov V.I Quasidifferentials in experiment design problems. Proc. of the Russian Higher SchoolAcademy of Sciences. 2014; 4(25):124–136. (In Russ.)
13. Khabarov V.I. Kontseptual’naya model’ intellektual’noy sistemy planirovaniya i analiza eksperimentov [Conceptual model of intelligent system for designing and analyzing experiments]. Sistemy iskustvennogo intellekta. Novosibirsk: NETI; 1992: 3-15. (In Russ.)
14. Khabarov V., Berestov L., Denisov V., Kozlov A., Melnik V. Intelligent support of flight experimental designand analysis-artificial intelligence in applications of engineering. VI Intern. Symposium. Oxford; 1991:319–328.
15. Denisov V.I., Khabarov V.I. Arkhitektura integrirovannoy sistemy “EVM-eksperimentator” [Architecture of the integrated the “Computer-Experimenter” system]. Sbornik nauch. tr.: Mashinnye Metody Planirovaniya Eksperimenta i Optimizatsii Mnogofaktornykh Sistem. Novosibirsk: NETI; 1989:3–8. (In Russ.)
16. Denisov V.I., Poletaeva I.A., Khabarov V.I. Ekspertnaya sistema dlya analiza mnogofaktornykhob’ektov. Dispersionnyy analiz. Pretsedentnyy podkhod [Expert system for analyzing multi-factor objects. Analysis of variance. Case-based approach]. Novosibirsk: Novosibirskiy Elektrotekhnicheskiy Institut; 1992: 127. (In Russ.)
Bibliography link:
Khabarov V.I. Logical aspects of experimental design and analysis // Computational technologies. 2020. V. 25. ¹ 3. P. 142-151
|
