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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2022, Number 2, Pages 76–79
(Mi vmumm4466)
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Short notes
Embedding of the atomic theory of subsets of free semigroups to the atomic theory of subsets of free monoids
B. O. Konstantinovskiy, F. D. Kholodilov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
In this paper, we consider atomic formulas constructed from the binary predicate symbol $\subseteq$ and binary function symbols $\backslash$, $/$, $\cup$, and $\cap$. For $X$ and $Y$ from the powerset of a free semigroup, $X/Y$ denotes the set consisting of elements whose product with any element of $Y$ ( multiplying on the right) belongs to $X$. Similarly, one defines $Y \backslash X$ (multiplying on the left). We prove that every atomic formula that is true in every free semigroup powerset interpretation is also true in every free monoid powerset interpretation.
Key words:
Lambek calculus, Lambek calculus models, language models, free semigroup, free monoid.
Received: 09.04.2021
Citation:
B. O. Konstantinovskiy, F. D. Kholodilov, “Embedding of the atomic theory of subsets of free semigroups to the atomic theory of subsets of free monoids”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 2, 76–79; Moscow University Mathematics Bulletin, 77:2 (2022), 108–111
Linking options:
https://www.mathnet.ru/eng/vmumm4466 https://www.mathnet.ru/eng/vmumm/y2022/i2/p76
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Abstract page: | 42 | Full-text PDF : | 10 | References: | 17 | First page: | 1 |
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