Algebraic structure of hierarchical semantic networks
UDC
004.822Abstract
The mathematical description of hierarchical semantic networks class is specified. Such networks are natural as coherent semantic representations of logical-mathematical models of subject domain knowledge spaces. Such models are realized in format similar to G. Frege's triangle and D. Pospelov's square. The description is agreed with the unified format for abstract knowledge representation formalisms and includes sets of knowledge representations and knowledge fragments, operation of knowledge fragments composition and the relation of fragments inclusion. The system of requirements to the sets of the objects making networks and network fragments structures is specified. The algorithm of creation of any fragments of hierarchical networks from basic fragments of such networks by operation of composition is defined. Existence of algorithm of finding the shortest sequence of the composition operation that create any fragment of a network is proved. Any sequence of compositions defines algebraic structure of the received semantic network. That structure consists of network fragments ordered by relation of transformation possibility of one fragment of a network into another fragment. This relation is not the order relation on a set of fragments of semantic networks, but it is an order on a set of networks. Variants of monotony relations for composition and inclusions of semantic networks fragments are considered.
Keywords:
semantic network, knowledge composition, knowledge inclusion, knowledge fragment, algebraic structure, knowledge presentation formalismFunding information
Работа выполнена при поддержке РФФИ (13-01-96513).
References
- Костенко К.И. Компоненты и операции абстрактных пространств знаний. ЗОНТ09: Мат. Всерос. конф., Новосибирск, 20-22 октября, 2009 г., T. 2. С. 36-40. [Kostenko K.I. Komponenty i operatsii abstraktnykh prostranstv znaniy [Components and operations of the abstract spaces of knowledge]. In ZONT09: Mat. Vseros. konf., Novosibirsk, 20-22 oktyabrya, 2009. T. 2 [Proc. Russian Conf. 'ZONT09', 20-22 October, 2009], pp. 36-40. (In Russian)]
- Костенко К.И., Лебедева А.П. О формализованных описаниях пространств знаний // Программная инженерия. 2013. № 8. С. 25-34. [Kostenko K.I., Lebedeva A.P. O formalizovannykh opisaniyakh prostranstv znaniy [On formal descriptions of the spaces of knowledge]. Programmnaya inzheneriya [Software engineering], 2013, no. 8, pp. 25-34. (In Russian)]
- Чечкин А.В. Нейрокомпьютерная парадигма информатики // Нейрокомпьютеры: разработки, применение. 2011. № 7. С. 3-9. [Chechkin A.V. Neyrokomp'yuternaya paradigma informatiki [Neurocomputer paradigm of Informatics]. Neyrokomp'yutery: razrabotki, primenenie [Neurocomputers: development, application], 2011, no. 7, pp. 3-9. (In Russian)]
- Gupta A., Nishimura N. Finding largest subtrees and smallest supertrees // Algorithmica. 1998. Vol. 21. P. 183-210.
- Костенко К.И. Вложения формализмов семантических сетей // Экологический вестник научных центров Черноморского экономического сотрудничества. 2013, № 2. С. 58-66. [Kostenko K.I. Vlozheniya formalizmov semanticheskikh setey [Attachments formalisms of the semantic web]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of the scientific centers of the Black Sea Economic Cooperation], 2013, no. 2, pp. 58-66. (In Russian)]
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Copyright (c) 2014 Костенко К.И., Лебедева А.П.
This work is licensed under a Creative Commons Attribution 4.0 International License.
