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Prof. Alexander Fridman talks about how algebraic concepts can be used to analyze data and knowledge

Relationship Talk: How the Convergence of Algebra and Databases is Bringing to Light a New Wave of Intelligent Systems

By IGI Global on Mar 23, 2018
Book cover image
Prof. Boris Kulik
In this day and age, everything is data-driven. New technologies are being developed at a record pace and human beings are increasingly becoming dependent on them, generating more data than ever before. As a leading academic publisher, it is IGI Global's mission to take part in those innovations by collaborating with experts and researchers to publish groundbreaking concepts and theories. In this logic, in an interview with IGI Global, Professor Alexander Fridman from the Russian Academy of Science, Russia, and second co-author of the book N-ary Relations for Logical Analysis of Data and Knowledge, shared his thoughts and ideas of Dr. Boris Kulik, who has directed this research for 20 years, on computer science and mathematics.

What inspired you to pursue research activities in your research area?

Developers of modern intelligence systems face certain challenges resulting from fundamentally different approaches used in constructing databases (DB) and knowledge bases (KB). KB design is based on the theory of formal systems (TFS) while DBs are grounded by relational algebra (RA). This incompatibility results in significantly different programming systems and structures for DBs and KBs, and consequently, in big difficulties to integrate a DB and a KB within one software system. So, we strive for combining advantages and lowering drawbacks of both RA and TFS by extending algebraic techniques to a unified logical-semantic analysis of data and knowledge.

Why are your respective areas of research important to the field at large?

The novelty of our approach is that we developed some new mathematical structures allowing to realize many techniques of semantic and logical analyses; these methods have no analogies in convenient theories. Our n-tuple algebra (NTA) belongs to the class of Boolean algebras. Unlike RA and theory of binary relations, NTA uses the Cartesian product of sets rather than sequences of elements (elementary n-tuples) as a basic structure and implements general theory of n-ary relations. This approach can become topical for different fields of artificial intelligence due to its following features. NTA is proved to be isomorphic to algebra of sets. It uses the same operations (union, intersection, complement) and relations (equality and inclusion) completed with simple operations on attributes (renaming, transposition and elimination of attributes; in addition of a dummy attribute). Despite its seeming primality, NTA provides modeling the following formats of data and knowledge: relational models; graphs and networks; models of propositional and predicate calculi; systems of artificial intelligence (expert rules, semantic networks, frames and ontologies); models of deductive and abductive reasoning; logic-probabilistic methods including probabilistic logic; discrete automata; models to solve Constraint Satisfaction Problem (CSP); question-answer systems.

Book cover image
Prof. Alexender Fridman
In your opinion, what are some of the benefits of your research to its community of users?

The proposed representation of relations by means of Cartesian products allows the application of an algebraic approach not only in database management systems (DBMSs), such as relational DBMSs, deductive databases, etc., but also in knowledge systems (systems for commonsense reasoning and so on). This is a practical idea because the representation reduces the computational complexity of logical analysis in many cases. A practicable logical analysis should include both deduction (logical inference) and non-deductive analysis techniques, i.e. analyzing uncertainties and inconsistency, as well as forming hypotheses and abductive conclusions. Convenient formal methods of the classical approach provide a solution to the deductive tasks only, with some other problems arising regardless. Other mentioned tasks commonly involve non-classical logics, in particular, the default logic and non-monotonic logics. It is not easy to combine logical inference and non-deductive reasoning within the formal approach. Our general theory of relation provides some possibilities to merge deductive and defeasible analysis.



What are the future directions of your research areas?

We plan to conduct future research in the following directions: context-oriented database (knowledge base) management systems; additional means of immersing NTA structures into measure spaces and assigning NTA objects with quantitative features; modeling dynamic intelligent systems within the situational approach.

What are some other evolving research trends you have observed in your industry/field over the past several months and what would you say are some of the innovative research directions you foresee in the future? How do you feel your publication sets the pace for these innovations?

To our minds, most impressive research has been accomplished in the fields of robotics, data mining, pattern recognition and machine learning. These fields are far from our area of interest, so we do not comment them. As for reasoning systems where we work, there development seems to become slower due to a lack of new ideas to model human way of argumentation. We believe algebraic techniques can provide a promising path for this kind of research.

IGI Global is grateful for the opportunity to work with Prof. Fridman and we look forward to seeing more collaboration that will result in the publication of invaluable content like his book, N-ary Relations for Logical Analysis of Data and Knowledge. We would like to thank Prof. Boris Kulik from the Russian Academy of Science, Russia, who is also the lead author of the book, and Prof. Fridman for helping IGI Global cultivate and disseminate emerging concepts and theories in Computer Science and Information Technology.
For more information please see Prof. Fridman's book, along with the following related publications, and recommend them to your library.

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