Formal theory model in the form of commutative semigroup of image constructions

• Дата: 2015
• Автори: Бисикало, Олег Владимирович, Кравчук, Ирина Анатольевна, Кириленко, Анна Александровна
• Формат: Стаття
• Мова: Russian
• Опубліковано: Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2015
• Теми: 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; формальна теорія; комутативна напівгрупа; мовний образ; образна конструкція; підтримка діалогу
• Онлайн доступ: https://journals.uran.ua/jme/article/view/21315
• Назва журналу: Energy Technologies & Resource Saving

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.