In this paper, we formalize the general concept of a document model in terms of the Semantic Modelling (SM) paradigm. We argue that the idea of using documents as a basic metaphor for modelling appears to be very useful, since it provides a balance between the logical tools for knowledge processing and cognitive aspects for a much wider audience than the community of professional mathematicians. A subject domain can be arbitrarily complex by its nature, but humans tend to choose those primitives, which are convenient for cognition. The notion of a document is an example of such a primitive, which has been employed for centuries and clearly remains topical in the era of information systems. The significant outcome of constructing the semantics of document models within the SM paradigm is that Semantic Modelling makes document models executable. Executable models can be directly used as practical information systems, and this feature makes the programming stage unnecessary. Replacing programming with modelling has a great impact on the efficiency of IT systems development and maintenance, and makes these systems friendly for the Artificial Intelligence tools.

Andrei Mantsivoda, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, Sobolev Institute of Mathematics, 4, Acad. Koptyug st., Novosibirsk, 630090, Russian Federation, e-mail: andrei@baikal.ru

Denis Ponomaryov, Cand. Sci. (Phys.–Math.), Ershov Institute of Informatics Systems, Sobolev Institute of Mathematics, Novosibirsk State University, 6, Lavrentyev av., Novosibirsk, 630090, Russian Federation, e-mail: ponom@iis.nsk.su

Mantsivoda A.V., Ponomaryov D.K. A Formalization of Document Models with Semantic Modelling. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 27, pp. 36-54. https://doi.org/10.26516/1997-7670.2019.27.36

1. Ershov Yu.L., Goncharov S.S., Sviridenko D.I. Semantic Programming. Information processing 86: Proc. IFIP 10th World Comput. Congress. 1986, vol. 10, Elsevier Sci., Dublin, pp. 1093-1100.
2. Ershov Yu.L., Goncharov S.S., Sviridenko D.I. Semantic Foundations of Programming. Fundamentals of Computation Theory: Proc. Intern. Conf. FCT 87, Kazan, Lect. Notes Comp. Sci., 1987, vol. 278. pp. 116-122. https://doi.org/10.1007/3-540-18740-5_28 
3. Goncharov S.S., Sviridenko D.I. Σ-programming. Transl. II. Amer. Math. Soc., 1989, no. 142, pp. 101-121.
4. Goncharov S.S., Sviridenko D.I. Σ-programming and its Semantics. Vychisl. Systemy, 1987, no. 120, pp. 24-51. (in Russian).
5. Goncharov S.S., Sviridenko D.I. Theoretical Aspects of Σ-programming. Lect. Notes Comp. Sci., 1986, vol. 215, pp. 169-179. https://doi.org/10.1007/3-540-16444-8_13
6. Goncharov S.S. Conditional Terms in Semantic Programming. Siberian Mathematical Journal, 2017, vol. 58, no. 5, pp. 794-800. https://doi.org/10.1134/S0037446617050068
7. Kazakov I.A., Kustova I.A., Lazebnikova  E.N., Mantsivoda  A.V. Building locally simple models: theory and practice. The Bulletin of Irkutsk State University. Series Mathematics, 2017, vol. 21, pp. 71-89. (in Russian). https://doi.org/10.26516/1997-7670.2017.22.71
8. Malykh A.A., Mantsivoda A.V. Document Modelling. The Bulletin of Irkutsk State University. Series Mathematics, 2017, vol. 21, pp. 89-107. (in Russian). https://doi.org/10.26516/1997-7670.2017.21.89
9. Ospichev S., Ponomarev D. On the Complexity of Formulas in Semantic Programming. Siberian Electronic Mathematical Reports, 2018, vol. 15, pp. 987–995.
10. Pirri F. and Reiter R. Some Contributions to the Metatheory of the Situation Calculus. J. ACM, 1999, vol. 46, no. 3, pp. 325–364.
11. Reiter R. Knowledge in Action: Logical Foundations for Describing and Implementing Dynamical Systems. MIT Press, 2001. https://doi.org/10.7551/mitpress/4074.001.0001
12. E. Vityev. Semantic Probablistic Inference of Predictions. The Bulletin of Irkutsk State University. Series Mathematics, 2017, vol. 21, pp. 33-50. (in Russian).