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Unranked Fuzzy Logic and its Applications (YS-19-367)


Funded by

SRNSFGShota Rustaveli National Science Foundation of Georgia

Start Date: 2019-12-11       End Date: 2021-12-11

One of the main tools in knowledge representation is ontology, which is a collection of logic-based formal language sentences. These sentences are used by automated reasoning programs to extract new knowledge and answer to the given questions.
Although ontology languages are standardized by W3C, there are still many problems remaining. One of the most important problem is related to, so called, fuzzy ontologies. These are ontologies, where information is vague and imprecise. Fuzzy ontologies are obtained by integrating fuzzy logic with ontologies. Such kind of ontologies have applications in many different fields, such as medicine, biology, e-commerce and the like.
The aim of the proposed project is to develop an unranked fuzzy logic, study its properties and introduce reasoning methods for it. The novelty of our approach is that we will extend many-valued logics with sequence variables and flexible-arity function symbols. To the best of our knowledge, such formalisms are not yes studied in the literature. Unranked fuzzy language will broaden the knowledge engineering capabilities in different fields.
The expected results are both of theoretical and practical character. Its scientific value can be assessed by the fact that it will be an important step forward into combining fuzzy and unranked formalisms. Merging flexibility of unranked formalisms on the one hand, and the efficient way of dealing with vagueness provided by fuzzy terms will result into an improved, powerful, high-level technique and tool with a great potential for ontology engineering and knowledge modeling tasks.
From the expected practical results it is worth to mention development of software realization of unranked fuzzy language and corresponding reasoning methods. We experiment with the system and study its use cases in other fields.

Project members:

Talks

  • Towards Unranked Fuzzy Theory, by Mikheil Rukhaia (Speaker), Anriette Michel Fouad Bishara at IEEE International Conference on System Analysis & Intelligent Computing, 2020, Kiev, Ukraine (online).
  • Unranked Fuzzy Logic and its Applications, by Mikheil Rukhaia (Speaker) at XXXIV Enlarged Sessions of the Seminar of I.Vekua Institute of Applied Mathematics, 2020, Tbilisi, Georgia (online).
  • Unranked Fuzzy Reasoning, by Anriette Michel Fouad Bishara (Speaker), Mikheil Rukhaia at XXXV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, 2021, Tbilisi, Georgia (online).
  • About Terminating Unranked Fuzzy Tableaux, by Mikheil Rukhaia (Speaker), Anriette Michel Fouad Bishara at 34th BARCELONA International Conference on Futuristic Trends in Science, Engineering & Technology, 2021, Barcelona, Spain.
  • About Unranked Fuzzy Unification, by Mikheil Rukhaia (Speaker), Anriette Michel Fouad Bishara at XI Annual International Conference of Georgian Mathematical Union, 2021, Batumi, Georgia.
  • A Fuzzy Logic with Sequence Variables and Flexible-arity Symbols, by Mikheil Rukhaia (Speaker), Anriette Michel Fouad Bishara at Proof Society Workshop on Proof Theory and its Applications, 2021, Funchal, Madeira, Portugal.

Publications

  • Mikheil Rukhaia, Anriette Michel Fouad Bishara, Towards Unranked Fuzzy Theory, In proceedings of IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC 2020), IEEE, 2020.
  • Mikheil Rukhaia, Anriette Michel Fouad Bishara, Unranked Fuzzy Logic and Reasoning, In: Zgurovsky, M., Pankratova, N. (eds) System Analysis & Intelligent Computing: Theory and Applications. Studies in Computational Intelligence, vol 1022, pp.339-353, Springer, 2022.
  • Besik Dundua, Temur Kutsia, Mikheil Rukhaia, Unranked Nominal Unification, In: Özgün, A., Zinova, Y. (eds) Language, Logic, and Computation. TbiLLC 2019. Lecture Notes in Computer Science, vol 13206, pp.279-296, Springer, 2022.

Additional Information

Under the project we have implemented unranked fuzzy logic. It was a master project of Merihan Hazem Anwar Labib Bishara. The code is available here.