**Abstract**
“The problem of understanding of intelligence is said to be

the greatest problem in science today and “the” problem for

this century – as deciphering the genetic code was for the

second half of the latest one.

Arguably, the problem of learning represents a gateway to

understanding intelligence in brains and machines, to

discovering how the human brain works and to making

intelligent machines that learn from experience and improve

their competence…"

THE MATHEMATICS OF LEARNING:

DEALING WITH DATA

T. Poggio, S. Smale, Notices AMS, Vol. 50, May 2003 [185]

The Rasiowa–Pawlak school was established during the second half of the twentieth century. The school concentrates on studies in logics, foundations of computer science and artificial intelligence (AI). Its formation has been greatly influenced by the logician Andrzej Mostowski, a professor at Warsaw University [110,111], who, in particular, directed the doctoral dissertation of Helena Rasiowa. Nowadays, the disciples of the Rasiowa–Pawlak school are active in many research-development centres worldwide. The school founded its own journal, Fundamenta Informaticae. In this paper, we present selected trends in the studies of the school concerning applications of logic in AI. At the beginning, we briefly describe the genesis of the Rasiowa–Pawlak school. We then present the understanding, currently dominating within the school, on such basic concepts as AI and logic. Since the beginning of the 1950's, the focus of the research by Helena Rasiowa and her associates has been the application of algebraic and topological methods to the investigation of crucial problems of logic from an AI perspective. Amongst them are the completeness theorem, construction of deduction systems, construction of models, especially models for constructive mathematics [136,241,67] and related logics such as intuitionistic, intermediate, modal, and approximation logics. In the paper, we discuss the fundamental, in our opinion, ideas underlying these roots of the Rasiowa–Pawlak school. A great importance in the studies of the school is assigned to the search for optimal tools for reasoning about complex vague concepts, construction of knowledge representation systems, reasoning about knowledge as well as for the application of logics in learning, communication, perception, planning, action, cooperation, and competition.

It should be noted that as is the case with many other research centers, the Rasiowa– school studies pertaining to the application of logics in AI have also undergone an evolution which we present in this paper. We include extensive references to the literature on the approach presented in this paper.