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Automatic Documentation and Mathematical Linguistics

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01-04-2023 | INTELLIGENT SYSTEMS

Existence of Large Sublattices Isomorphic to Boolean Algebra in a Candidate Lattice

Author: D. Vinogradov

Published in: Automatic Documentation and Mathematical Linguistics | Issue 2/2023

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Abstract—

Algebraic machine learning has emerged as a way to overcome the need to generate a (potentially exponential) lattice of all candidates (as, for example, in the case of Boolean algebra). In this paper, it is proven that for a random training sample generated by the Bernoulli sequence, the probability that a large sublattice will arise in the lattice of candidates isomorphic to Boolean algebra will tend to unity as the sample size increases.

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DSM-metod avtomaticheskogo porozhdeniya gipotez. Logicheskie i epistemologicheskie osnovaniya (JSM Method of Authomatic Hypothesis Generation: Logical and Epistemological Foundations), Anshakov, O.M. and Finn, V.K., Eds., Moscow: URSS, 2009.

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Title: Existence of Large Sublattices Isomorphic to Boolean Algebra in a Candidate Lattice
Author: D. Vinogradov
Publication date: 01-04-2023
Publisher: Pleiades Publishing
Published in: Automatic Documentation and Mathematical Linguistics / Issue 2/2023
Print ISSN: 0005-1055
Electronic ISSN: 1934-8371
DOI: https://doi.org/10.3103/S0005105523020097

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Existence of Large Sublattices Isomorphic to Boolean Algebra in a Candidate Lattice

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