Formal theory model in the form of commutative semigroup of image constructions
The paper deals with the issues of creating the mathematical apparatus for dialogue support with user, based on information generalization of each sentence in the text by the formal concept of linguistic image. Relevance of the research issues is associated with ensuring stepwise finding of the requ...
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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Russian |
| Опубліковано: |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України
2015
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| Онлайн доступ: | https://journals.uran.ua/jme/article/view/21315 |
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| Назва журналу: | Energy Technologies & Resource Saving |
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oai:ojs.journals.uran.ua:article-213152024-09-01T17:33:33Z Formal theory model in the form of commutative semigroup of image constructions Модель формальной теории в виде коммутативной полугруппы образных конструкций Модель формальної теорії у вигляді комутативної напівгрупи образних конструкцій Бисикало, Олег Владимирович Кравчук, Ирина Анатольевна Кириленко, Анна Александровна formal theory commutative semi-group linguistic image image construction dialogue support УДК 004.93 159.95 формальная теория коммутативная полугруппа языковый образ образная конструкция поддержка диалога УДК 004.93 159.95 формальна теорія комутативна напівгрупа мовний образ образна конструкція підтримка діалогу УДК 004.93 159.95 The paper deals with the issues of creating the mathematical apparatus for dialogue support with user, based on information generalization of each sentence in the text by the formal concept of linguistic image. Relevance of the research issues is associated with ensuring stepwise finding of the required specialized information during training and professional development of modern engineers within the question-answering systems.Assuming syntactic relations between all meaningful words of each sentence and linguistic images, corresponding to these words are known, formal first-order theory was proposed The finite alphabet, procedures for constructing terms as character lines and formulas as admissible expressions of the formal theory \[Th\] were introduced into the theory structure. The axiom schemes such as 3 propositional calculus, 2 first-order predicate calculus, as well as proper axioms \[Th\] such as 6 commutative semi-groups and 4 applied axioms (productions) of the theory were singled out from many formulas. The concept of the term in the associative normal form (ANF) was introduced. Three theorems, allowing to convert any term into the ANF-term and any ANF-term into the question-answering structure of terms, and to present the ANF-term of the answering structure in the form of components (subtrees) from different sentences (trees) were formulated and proved.The formal theory model \[Th\] was proposed as the commutative semi-group of image constructions; linguistic interpretation and model limitations were considered. Three rules were introduced for easy use of the formal theory model \[Th\] in linguistic applications. The research results allow to provide basic support functions for the dialogue, limited by the linguistic image concept at the formal level. Работа посвящена созданию математического аппарата для поддержки диалога с пользователем на основе обобщения информации предложений текста. Разработана формальная теория первого порядка, предполагающая построение модели в виде коммутативной полугруппы конструкций из языковых образов. На основе 15-ти аксиом сформулированы и доказаны теоремы, позволяющие обеспечить базовые функции поддержки ограниченного понятием языкового образа диалога. Робота присвячена створенню математичного апарату для підтримки діалогу з користувачем на основі узагальнення інформації речень тексту. Розроблено формальна теорія першого порядку, що припускає побудову моделі у вигляді комутативної напівгрупи конструкцій мовних образів. На основі 15-ти аксіом сформульовані і доведені теореми, що дозволяють забезпечити функції підтримки обмеженого поняттям мовного образу діалогу. Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2015-04-01 Article Article application/pdf https://journals.uran.ua/jme/article/view/21315 Journal of Mechanical Engineering; Vol. 16 No. 6 (2013); 24-40 Проблемы машиностроения; Том 16 № 6 (2013); 24-40 Проблеми машинобудування; Том 16 № 6 (2013); 24-40 2709-2992 2709-2984 ru https://journals.uran.ua/jme/article/view/21315/36479 Copyright (c) 2015 Олег Владимирович Бисикало, Ирина Анатольевна Кравчук, Анна Александровна Кириленко https://creativecommons.org/licenses/by-nd/4.0 |
| institution |
Energy Technologies & Resource Saving |
| collection |
OJS |
| language |
Russian |
| topic |
formal theory commutative semi-group linguistic image image construction dialogue support УДК 004.93 159.95 формальная теория коммутативная полугруппа языковый образ образная конструкция поддержка диалога УДК 004.93 159.95 формальна теорія комутативна напівгрупа мовний образ образна конструкція підтримка діалогу УДК 004.93 159.95 |
| spellingShingle |
formal theory commutative semi-group linguistic image image construction dialogue support УДК 004.93 159.95 формальная теория коммутативная полугруппа языковый образ образная конструкция поддержка диалога УДК 004.93 159.95 формальна теорія комутативна напівгрупа мовний образ образна конструкція підтримка діалогу УДК 004.93 159.95 Бисикало, Олег Владимирович Кравчук, Ирина Анатольевна Кириленко, Анна Александровна Formal theory model in the form of commutative semigroup of image constructions |
| topic_facet |
formal theory commutative semi-group linguistic image image construction dialogue support УДК 004.93 159.95 формальная теория коммутативная полугруппа языковый образ образная конструкция поддержка диалога УДК 004.93 159.95 формальна теорія комутативна напівгрупа мовний образ образна конструкція підтримка діалогу УДК 004.93 159.95 |
| format |
Article |
| author |
Бисикало, Олег Владимирович Кравчук, Ирина Анатольевна Кириленко, Анна Александровна |
| author_facet |
Бисикало, Олег Владимирович Кравчук, Ирина Анатольевна Кириленко, Анна Александровна |
| author_sort |
Бисикало, Олег Владимирович |
| title |
Formal theory model in the form of commutative semigroup of image constructions |
| title_short |
Formal theory model in the form of commutative semigroup of image constructions |
| title_full |
Formal theory model in the form of commutative semigroup of image constructions |
| title_fullStr |
Formal theory model in the form of commutative semigroup of image constructions |
| title_full_unstemmed |
Formal theory model in the form of commutative semigroup of image constructions |
| title_sort |
formal theory model in the form of commutative semigroup of image constructions |
| title_alt |
Модель формальной теории в виде коммутативной полугруппы образных конструкций Модель формальної теорії у вигляді комутативної напівгрупи образних конструкцій |
| description |
The paper deals with the issues of creating the mathematical apparatus for dialogue support with user, based on information generalization of each sentence in the text by the formal concept of linguistic image. Relevance of the research issues is associated with ensuring stepwise finding of the required specialized information during training and professional development of modern engineers within the question-answering systems.Assuming syntactic relations between all meaningful words of each sentence and linguistic images, corresponding to these words are known, formal first-order theory was proposed The finite alphabet, procedures for constructing terms as character lines and formulas as admissible expressions of the formal theory \[Th\] were introduced into the theory structure. The axiom schemes such as 3 propositional calculus, 2 first-order predicate calculus, as well as proper axioms \[Th\] such as 6 commutative semi-groups and 4 applied axioms (productions) of the theory were singled out from many formulas. The concept of the term in the associative normal form (ANF) was introduced. Three theorems, allowing to convert any term into the ANF-term and any ANF-term into the question-answering structure of terms, and to present the ANF-term of the answering structure in the form of components (subtrees) from different sentences (trees) were formulated and proved.The formal theory model \[Th\] was proposed as the commutative semi-group of image constructions; linguistic interpretation and model limitations were considered. Three rules were introduced for easy use of the formal theory model \[Th\] in linguistic applications. The research results allow to provide basic support functions for the dialogue, limited by the linguistic image concept at the formal level. |
| publisher |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України |
| publishDate |
2015 |
| url |
https://journals.uran.ua/jme/article/view/21315 |
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