In the development of artificial intelligence, statistical and logical methods or their combination are primarily used. Logical methods play an important role in automated reasoning, one of the main cores of which is the knowledge representation in a language understandable to the machine. The main tool for the formal knowledge representation is ontologies, which are a set of propositions in a formal language based on logic. Automated reasoning modules use such sets of formal propositions to draw conclusions and provide answers to posed questions from the given information.
The goal of the project was to formulate the problems of unification and matching for probabilistic ontologies and to find and compare algorithms to solve them. Additionally, for those problems for which no solving algorithm exists, the study of algebraic structures induced by Turing and other algorithmic reductions.
The results of the project could be significant from the perspective of technical progress. Among the potential applications of the results, we would like to mention contributions to semantic web, which would facilitate data processing under conditions of uncertain and noisy information. We also believe that the direct application of the results may be useful in fields like knowledge modeling in medicine, biology, and others.
The results obtained from the project may be used in master's/doctoral courses in mathematical logic, theoretical computer science, and algebra, which will contribute to the international visibility and prestige of the Georgian scientific community. This will increase the interest of the international audience and create a foundation for future collaboration, both in scientific projects and in exchange programs for doctoral students and researchers.

Project members:

• Roland Omanadze (Principal Investigator)

• Mikheil Rukhaia (Key Personnel)

• Irakli Chitaia (Key Personnel)