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On Rank r Empirical Regularities in the JSM Method of Automated Research Supporta

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Automatic Documentation and Mathematical Linguistics Aims and scope

Abstract

The article deals with extensions of empirical regularities (ER) for r periods, where r > 1. Various types of ER constitute a lattice. Sequences of ER types correspond in a one-to-one manner to sequences of empirical modalities which form partially ordered semigroups. Syntactic and semantic types of ER are defined for the elements of these semigroups. The equality of semantic ER types that represent two different methods of extending fact bases determine the pragmatic condition for the acceptance of ER hypotheses.

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Notes

  1. The definitions of similarity, difference and similarity-difference predicates formalize in the JSM method of ARS the corresponding inductive inference rules of J.S. Mill in [27].

  2. Omitting the index σ, we obtain I = {a, ab, ae, aeb, af, afb}.

  3. The definition of the predicate H3({V1, … , Vm}, Y, p, h) is given in the Appendix of the paper to be published in Automatic Documentation and Mathematical Linguistics in 2024 (no. 2).

  4. Df. 3 and Df. 4 are to be found in the article Finn, V.K., On empirical regularities in the JSM method of automated research support, Autom. Doc. Math. Linguis., 2023, vol. 57, no. 6, pp. 362–381. https://doi.org/10.3103/S0005105523060055

  5. In practical application of the JSM method in intelligent systems, a slight change in the number s of fact bases is possible.

  6. It is also required to consider the codes \({\text{ER}}_{1}^{r}\) for Strx, y JSM reasoning strategies containing the addition of e (difference) and f (similarity-difference).

  7. Perhaps ER3 is a step towards independence of the existence of ERs from the way fact bases are expanded.

  8. We will also use the designations Sem Ts (\(\bar {Y}\)) and Sem Tw (\(\bar {Y}\)), where \(\bar {Y}\) is the word representing the ERi.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia

    V. K. Finn

  2. Russian State University for the Humanities, Moscow, Russia

    V. K. Finn

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Translated by V. Tereshchenko

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aThis article is a continuation of the publication Finn, V.K., On empirical regularities in the JSM method of automated research support, Autom. Doc. Math. Linguis., 2023, vol. 57, no. 6, pp. 362–381. https://doi.org/10.3103/S0005105523060055

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Finn, V.K. On Rank r Empirical Regularities in the JSM Method of Automated Research Supporta. Autom. Doc. Math. Linguist. 58, 10–31 (2024). https://doi.org/10.3103/S0005105524010035

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