Statement of Purpose by Vassilis G. Kaburlasos
Modeling human intelligence and Human-Machine-Interaction (HMI). Applications towards the development of competitive industrial products and services. Global scientific actions and initiatives.
The scientific framework is described in the following.
With the proliferation of computing devices, as well as of information technologies, a variety of domain-specific information processing paradigms has appeared in different application domains including signal/image processing, system modeling, machine learning, data mining, knowledge representation, pattern analysis, logic and reasoning, symbol manipulation, etc. The corresponding mathematical tools are, frequently, different also due to the need to cope with disparate types of data including matrices of (real) numbers, logic values, sets, (distribution) functions, data structures, (strings of) symbols, etc. A unification of the aforementioned tools is expected to result in a fruitful cross-fertilization of technologies. However, what is currently missing is an "enabling" mathematical framework.
It turns out that popular types of data, including the aforementioned ones, are lattice(partially)-ordered. Hence, lattice theory (LT) emerges as such an "enabling" mathematical framework for sound analysis and design involving numeric and/or nonnumeric data. Note that mathematical lattices were introduced in the first half of the nineteenth century as a spin off of work on formalizing propositional logic. Currently, in addition to being a branch of applied mathematics, LT emerges as an instrument in information engineering.
Statistical evidence strongly suggests that the work of researchers, who employ LT, is "diversified" in the sense that it, often, involves several different application domains. The aforementioned diversification may be explained in view of the unifying character of LT. Hence, in addition to its potential in general system studies including the study of (binary) relations, especially promising applications of LT are in inherently multidisciplinary domains such as human-computer-interaction (HCI), multimedia, cognitive robotics, etc.