Formal theory model in the form of commutative semigroup of image constructions
Keywords:
formal theory, commutative semi-group, linguistic image, image construction, dialogue supportAbstract
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 proposedThe 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.References
Turing, A. Computing Machinery and Intelligence [Text] / A. Turing // Mind. – 1950. – Vol. LIX, № 236. – P. 433 – 460. 2. Galitsky, B. Natural Language Question Answering System: Technique of Semantic Headers [Text] / B. Galitsky // International Series on Advanced Intelligence. – Australia: Advanced Knowledge International. – 2003. – Vol. 2. – Р. 12-20. 3. Бисикало, О. В. Ассоциативный поиск для задач обучения на основе электронного тезауруса образов [Текст] / О. В. Бисикало // Управляющие системы и машины. – 2009. – № 2. – С. 28 – 33. 4. Бісікало, О. В. Формалізація понять мовного образу та образного сенсу природно-мовних конструкцій [Text] / О. В. Бісікало // Математичні машини і системи. – 2012. – № 2. – С. 70 – 73. 5. Крылов, С. А. Некоторые уточнения к определениям понятий словоформы и лексемы [Текст] / С. А. Крылов // Семиотика и информатика. – 1982. – Вып. 19. – С. 118 – 136. 6. Бісікало, О. В. Формальні методи образного аналізу та синтезу природно-мовних конструкцій [Текст]: монографія / О. В. Бісікало. – Вінниця: Вінниць. нац. техн. ун-т, 2013. – 316 с. 7. Бодянский, Е. Классификация текстовых документов с помощью нечеткой вероятностной нейронной сети / Е. Бодянский, Н. Рябова, О. Золотухин // Восточно-Европейский журнал передовых технологий. – 2011. – T. 6, № 2(54). – С. 16 – 18. – Режим доступу: http://journals.uran.ua/eejet/article/view/1917 8. Соснин, П. И. Вопросно-ответное программирование человеко-компьютерной деятельности [Текст] / П. И. Соснин. – Ульяновск: Ульянов. техн. ун-т, 2010. – 240 с. 9. Чмир, І. О. Моделювання та синтез діалогових агентів в інтелектуальних системах [Текст] : автореф. дис. д-ра техн. наук: 05.13.23 / І. О. Чмир. – Київ, 2008 . – 33 с. 10. Burger, J. Tasks and Program Structures to Roadmap Research in Question & Answering (Q & A) [Text] /J. Burger, C. Cardie, V. Chaudhri et al. – New York, 2001. – P. 1 – 35. 11. Grillet, P. A. Commutative Semigroups [Text] / P. A. Grillet // Dordrecht: Kluwer Academic Publishers, 2001. – 440 p. 12. Горюшкин, А. П. Элементы абстрактной и компьютерной алгебры [Текст] : уч. пос. / А. П. Горюш-кин, В. А. Горюшкин. – 2-е изд., испр. и доп. – Петропавловск-Камчатский : КамГУ им. Витуса Беринга, 2011. – 518 с. 13. Clifford, A. H., Preston, G. B. The Algebraic Theory of Semigroups [Text] / A. H. Clifford, G. B. Preston // American Mathematical Soc., 1967. – 352 p. 14. Grillet, P. A. Semigroups: An Introduction to the Structure Theory [Text] / P. A. Grillet. – CRC Press, 1995. – 408 p. 15. Rosenfeld, V. Using Semigroups in Modeling of Genomic Sequences [Text] / V. Rosenfeld // MATCH Communications in Mathematical and in Computer Chemistry. – 2006. – Vol. 56. – P. 281 – 290. 16. Столл, Р. Множества. Логика. Аксиоматические теории [Text] : пер с англ. – М.: Просвещение, 1968. – 231 с. 17. Bisikalo, O. Formalization of semantic network of image constructions in electronic content [Электронный ресурс] / O. Bisikalo, I. Kravchuk // Cornell University Library (Computer Science, Computation and Language), arXiv: 1201.1192v1. – January 2012. – 4 р. – Aviable at: http://arxiv.org/ftp/arxiv/papers/1201/1201.1192.pdf. – 10.12.2013 г. – Загл. с экрана. 1. Turing, A. M. (1950). Computing machinery and intelligence. Mind, 59, 460. 2. Galitsky, B. (2003). Natural Language Question Answering System: Technique of Semantic Headers. Ad-vanced Knowledge International, Vol. 2, 12-20. 3. Bisikalo, O. V. (2009). Assotsiativnyy poisk dlya zadach obucheniya na osnove elektronnogo tezaurusa obrazov. Upravlyayushchiye sistemy i mashiny, 2, 28–33. 4. Bisikalo, O. V. (2012). Formalizatsiya ponyat movnogo obrazu ta obraznogo sensu pryrodno-movnykh konstruktsiy. Matematychni mashyny i systemy, 2, 70–73. 5. Krylov, S. A. (1982). Nekotoryye utochneniya k opredeleniyam ponyatiy slovoformy i leksemy. Semiotika i informatika, 19, 118–136. 6. Bisikalo, O. V. (2013). Formalni metody obraznoho analizu ta syntezu pryrodno-movnykh kon-struktsiy. Vinnitsya: VNTU, 316. 7. Bodyanskiy, E., Ryabova, N., Zolotukhin, O. (2012). Classification of text documents using the fuzzy probabilistic neural network. Eastern-European Journal Of Enterprise Technologies, 6 (2(54)), 16–18. Available at: http://journals.uran.ua/eejet/article/view/1917 8. Sosnin, P. I. (2010). Voprosno-otvetnoye pro-grammirovaniye cheloveko-kompyuternoy deyatelnosti. Uly-anovsk: UlGTU, 240. 9. Chmyr, І. О. (2008). Modelyuvannya ta syntez dialohovykh ahentiv v intelektualnykh systemakh. Kyiv, 33. 10. Burger, J., Cardie, C., Chaudhri, V. (2001). Is-sues, Tasks and Program Structures to Roadmap Research in Question & Answering (Q & A). New York: NIST, 1-35. 11. Grillet, P. A. (2001). Commutative Semigroups. Dordrecht: Kluwer Academic Publishers, 440. 12. Goryushkin, А. P., Goryushkin, V. А. (2011). Elementy abstraktnoy i kompyuternoy algebry. Petropav-lovsk-Kamchatsky: КаmGU im. Vitusa Beringa, 518. 13. Clifford, A. H., Preston, G. B. (1967). The Al-gebraic Theory of Semigroups. American Mathematical Soc, 352. 14. Grillet, P. A. (1995). Semigroups: An Introduc-tion to the Structure Theory. New York: Marcel Dekker, 408. 15. Rosenfeld, V. (2006). Using Semigroups in Modeling of Genomic Sequences. MATCH Communications in Mathematical and in Computer Chemistry, 56, 281–290. 16. Stoll, R. (1968). Mnozhestva. Logika. Aksio-maticheskiye teorii. Мoscow: Prosveshcheniye, 231. 17. Bisikalo, O., Kravchuk, I. (2012). Formalization of semantic network of image constructions in electronic content. Cornell University Library (Computer Science, Computation and Language), arXiv: 1201.1192v1, 13. Avail-able at: http://arxiv.org/ftp/arxiv/papers/1201/1201.1192.pdf (accessed 10 December 2013).
Downloads
Published
Issue
Section
License
Copyright (c) 2015 Олег Владимирович Бисикало, Ирина Анатольевна Кравчук, Анна Александровна Кириленко
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
All authors agree with the following conditions:
- The authors reserve the right to claim authorship of their work and transfer to the journal the right of first publication of the work under the license agreement (the agreement).
- Authors have a right to conclude independently additional agreement on non-exclusive spreading the work in the form in which it was published by the jpurnal (for example, to place the work in institution repository or to publish as a part of a monograph), providing a link to the first publication of the work in this journal.
- Journal policy allows authors to place the manuscript in the Internet (for example, in the institution repository or on a personal web sites) both before its submission to the editorial board and during its editorial processing, as this ensures the productive scientific discussion and impact positively on the efficiency and dynamics of citation of published work (see The Effect of Open Access).
