**Plenary Lecture
Mathematical Models for Analogical Reasoning**

**Professor Michael Gr. Voskoglou**

School of Technological Applications

Graduate Technological Educational Institute (T. E. I.)

Patras, Greece

E-mail: voskoglou@teipat.gr

**Abstract: ** Analogical Reasoning (AR) is a method of processing information that compares the similarities between new and past understood concepts, then using these similarities to gain understanding of the new concept. The basic intuition behind AR is that when there are substantial parallels across different situations there are likely to be further parallels. AR is ubiquitous in human cognition. Analogies are used in explaining concepts which cannot directly perceived (e.g. electricity in terms of the water flow), in making predictions within domains, in communication and persuasion, etc. Within cognitive science mental processes are likened to computer programs (e.g. neural networks) and such analogies serve as mental models to support reasoning in new domains. AR is important in general in creativity and scientific discovery.

Several studies (Holyoak 1985, Genter & Toupin 1986, Novick 1988, Genter & Markman 1997, etc) have provided detailed models for the process of AR which are broadly consistent with reviews of problem solving strategy training studies, in which factors associated with instances of successful transfer – that is, use of already existing knowledge to produce new knowledge - are identified. According to these studies the main steps involved in AR include:

• Representation of the target problem.

• Search-retrieval of a related past problem.

• Mapping of the representations of the target and the related problem.

• Adaptation of the solution of the related problem for use with the target problem.

In this work we develop two mathematical models for the description of the process of AR: A stochastic model by introducing a finite ergodic Markov chain on the steps of the AR process and a fuzzy model by representing the main steps of the AR process as fuzzy subsets of a set of linguistic labels characterizing the individuals’ performance in each of these steps. The two models are compared to each other by listing their advantages and disadvantages. Experiments are also performed to illustrate their use in practice.

**Brief Biography of the Speaker: ** Michael Gr. Voskoglou (B.Sc., M.Sc., M.Phil. , Ph.D. in Mathematics) is a Professor of Mathematical Sciences at the Graduate Technological Educational Institute of Patras, Greece. He has also taught at the Hellenic Open University, at the Mathematics Department of the University of Patras, at TEI of Messolonghi, etc. As a visiting professor he has taught in M.Sc. courses of the department of Operational Mathematics at the University of Applied Sciences in Berlin and of the School of Management at the University of Warsaw, while he worked for 3 years (1997-2000) as a post doctoral researcher in the Bulgarian Academy of Sciences in Sofia (under sabbatical).

He is the author of 8 books (7 in Greek and 1 in English language) and of more than 260 papers published in reputed journals and proceedings of conferences of 22 countries in 5 continents, with many references from other researchers.

He is also the Editor in Chief and publisher of the “International Journal of Applications of Fuzzy Sets” (e-journal), reviewer of the American Mathematical Society and member of the Editorial Board or referee in several mathematical journals.

His research interests include Algebra, Fuzzy Sets, Markov Chains and Mathematics Education.