The science of mathematics was considered to be similar to the sciences of magic and occult during the Renaissance period. During this period, astrologer, mathematician, and conjurer were all considered to be the same thing. There was a lot of rhetoric associated with the study of mathematics. The importance of logic in the study of mathematics was not completely clear (Neal, Katherine). Helena Rasiowa spent her entire life working on mathematical logic.
Her thesis presented in 1950 was titled, Algebraic Treatment of the Functional Calculus of Lewis and Heyting, on the subject of algebra and logic. She led the Mathematical Logical Section of University of Warsaw when it was created in 1970 (O’Connor, J J. Robertson, E F). Her works include books on proof theory and deductive logic, use of algebraic methods in logic, how algebra is related to logic, algorithmic and approximation logics, classical and non-classical logics, and artificial intelligence (Bartol, W. Orlowska, E. Skowron, A. ).
Algebraic Logic – Rasiowa’s early work contained many examples of algebras related to logical systems alongside proofs of their algebraic properties. She presented for the first time the algebraic proof of the Godel completeness theorem for classical predicate logic together with Roman Sikorski. Then, she presented algebraic proof of analogous theorems for intuitionistic and modal logics. She worked on non-classical logics. Here, she applied the algebraic methods she had developed. She also worked on developing an algebraic presentation of propositional and first order logics.
She made important contributions in developing formal techniques for providing algebraic semantics of classes of algebra (Riddle, Larry). Mathematical Foundations of Computer Science – Helena Rasiowa made notable contributions to the research in Poland on using logical methods in computer science. She was among the first people to understand the significance of mathematical logic for computer science. Simultaneously, she also saw how computer science was important for the development of logic itself.
Many of her students later became notable authors of important works on logical and algebraic methods in computer science (Riddle, Larry). According to Helena Rasiowa, the students of mathematics usually do not develop the habit of clearly formulating the ideas to be expressed, to learn to reason methodically, and to understand the fundamental concepts of mathematics. She was of the view that these difficulties were due to three reasons. Firstly, due to insufficient training in mathematical logic.
She defined mathematical logic as the discipline whose task is to study deductive reasoning employed in proving mathematical theorems. The second reason was the ignorance of the basic concepts and methods used in set theory. Set theory is extensively applied to all branches of mathematics and serves as the basis for introducing and explaining fundamental mathematical concepts. Thirdly, the lack of knowledge of the basic concepts of abstract algebra. This knowledge is also essential for all branches of mathematics (Riddle, Larry).
It can be said that all her research belonged to mathematical logic and specifically to algebraic logic. As a progression from her work on non-classical logics in the 1970s, she moved on to logics related to the computational field. But, still the essence of this work was also related to algebraic logic (Font, J. M. ).
1999. Neal, Katherine. The Rhetoric of Utility: Avoiding Occult Associations for Mathematics Through Profitability and Pleasure, 154. Retrieved March 12, 2007 from www. shpltd. co. uk/neal-rhetoric. pdf 1997.O’Connor, J J. Robertson, E F. Helena Rasiowa. School of Mathematics and Statistics University of St. Andrews,Scotland. Retrieved March 12, 2007 from http://www-history. mcs. st-andrews. ac. uk/Biographies/Rasiowa. html n. d. Bartol, W. Orlowska, E. Skowron, A. Helena Rasiowa, 1917 – 1994, Retrieved March 13, 2007 from http://www. mimuw. edu. pl/%7Emrr/Rasiowa/RasiowaBiogr/RasiowaBiogr. htm May 5, 2006. Riddle, Larry. Helena Rasiowa. Biographies of Women Mathematicians. Retrieved March 13, 2007 http://www. agnesscott. edu/lriddle/women/rasiowa.
htm May 5, 2006. Riddle, Larry. Helena Rasiowa. Biographies of Women Mathematicians. Retrieved March 13, 2007 from http://www. agnesscott. edu/lriddle/women/abstracts/rasiowa_abstract. htm 1996. J. M. Font, “On the contributions of Helena Rasiowa to mathematical logic,” ismvl, p. 147, 26th International Symposium on Multiple-Valued Logic (ISMVL ’96). Retrieved March 13, 2007 from http://csdl2. computer. org/persagen/DLAbsToc. jsp? resourcePath=/dl/proceedings/&toc=comp/proceedings/ismvl/1996/7392/00/7392toc. xml&DOI=10. 1109/ISMVL. 1996. 508351