June 20, 1917 - August 9, 1994

Based on the article "Helena Rasiowa, 1917-1994" by W. Bartol, E. Orlowska, and A. Skowron from the Bulletin of the European Association for Theoretical Computer Science, Vol. 62 (1997), 353-366. Reprinted with permission of the EATCS.

Helena Rasiowa, mathematician and logician, passed away on August 9, 1994. Her influence on the shape of mathematical logic can hardly be overestimated.

She was born in Vienna on June 20, 1917 to very patriotic Polish parents. As soon as Poland had regained its independence in 1918 after more than a century of partitioned stateless existence, the whole family settled in Warsaw. Helena's father was a high-class railway specialist; his knowledge and experience in the field led him to assume very important positions in the railway administration. The girl, her parents' only child, had good conditions to grow up physically and mentally. And, indeed, she exhibited many different skills and interests, varying from music, which she was learning at a music school parallel to her normal studies in a secondary school, to business management, which she studied for more than a semester after completing her secondary education. But finally the most important of her interests, as the future was to prove, took the lead.

In 1938 the time was not very propitious for entering a university. Even if not many in Europe were convinced that war was inevitable, the next year was to prove how mistaken those of the majority were. Rasiowa had to interrupt her studies, for no legal education was possible in Poland after 1939. Many people fled the country, or at least they fled the big towns which were more subject to German bombardments and terror. So did the Ras family, also because of the fact that most high-ranking administration officials and members of the government were being evacuated to Romania. The Ras's spent a year in Lvov. After the Soviet invasion in September 1939 the town was taken over by the Soviet Union. The life of many Poles became endangered, so eventually the father decided to return to Warsaw.

Life was very restricted in Poland during the Nazi occupation. Nevertheless, there were enough courageous people to organize an underground life, not only for armed conspiracy against the Nazis, but also for the development of all the areas of a nation's life which are vital for its survival, education and, in particular, higher education among them. Thus Helena Rasiowa followed her studies in mathematics, risking her life, as did everybody who dared to conspire during that dark period.

Polish mathematics acquired particular strength in the pre-war years, mainly after the emergence of the Polish School of Mathematics in 1921. The names of Stefan Mazurkiewicz and Waclaw Sierpinski, who were in Warsaw, or those of Stefan Banach and Hugo Steinhaus, who were in Lvov, were well known to mathematicians all over the world. One of the branches which became important at that time besides functional analysis, set theory and topology, was logic, with researchers such as Jan Lukasiewicz, Stanislaw Lesniewski, Kazimierz Ajdukiewicz, Alfred Tarski and others.

Rasiowa became strongly influenced by Polish logicians. Still in conspiracy, she wrote her Master's thesis under the supervision of Jan Lukasiewicz and Boleslaw Sobocinski. History, however, turned against her once more. In 1944 the Warsaw Uprising broke out and in consequence Warsaw was almost completely destroyed, not only because of warfare, but also because of the systematic destruction which followed the uprising after it had been squashed down. Rasiowa's thesis was burned together with the whole house. She herself survived with her mother in a cellar covered by ruins of the demolished building.

After the war Polish mathematics, as all other areas of life, began to recover its institutions, its moods and its people. Many had been killed, many had died, many had left the country, but those who remained considered their duty the reconstruction of Polish science and universities. One of the important conditions for this reconstruction was to gather all those who could participate in recreating mathematics. Rasiowa had in the meantime accepted a teaching position in a secondary school. That is where she was discovered by Andrzej Mostowski and brought back to the University. She rewrote her Master's thesis in 1945 and in the next year she started her academic career as an assistant at the University of Warsaw, the institution she remained linked with for the rest of her life.

At this University she prepared and defended her Ph.D. thesis in 1950 (under the guidance of Prof. Andrzej Mostowski). The title of the thesis was "Algebraic treatment of the functional calculi of Lewis and Heyting" and it pointed to the main field of her future research, algebraic methods in logic. In 1956 she earned her second academic degree (equivalent to habilitation today) in the Institute of Mathematics of the Polish Academy of Sciences, where between 1954 and 1957 she held a post of Associate Professor jointly with an analogous position at the University, becoming Professor in 1957 and subsequently Full Professor in 1967. For the degree she submitted two papers: "Algebraic models of axiomatic theories" and "Constructive theories," which together formed a thesis named "Algebraic models of elementary theories and their applications."

Her interests were not limited to pure research. Always ready to cooperate with others and aware of the importance of a strong mathematical community, she participated in many forms of this community's activities. Since 1964 and till her retirement in 1993 she headed the section of Foundations of Mathematics and later of Mathematical Logic after its creation in 1970. For more than 15 years she was Dean of the Faculty of Mathematics, Computer Science and Mechanics (1958-1960, 1962-1966, 1968-1978). Strongly attached to the Polish Mathematical Society, she was its Secretary (1955-1957) and then Vice-President (1958-1959); in the Warsaw division of the Society she was elected President twice (1957-1959 and 1963-1965). In the Association for Symbolic Logic she was Council member (1958-1960) and member of the Executive Committee for European Affairs (1972-1977). She also was Alternate Assessor (1972-1975) and Assessor (1975-1979) in the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Sciences. On the other hand, she contributed to the development of mathematics in Poland as a member of the Committee on Mathematics of the Polish Academy of Sciences from 1961 until her very last days, and as a member and, for 20 years Chairperson, of the Group on Education and Research in Mathematics of the Ministry of Science and Higher Education. Since 1972 she was on the Scientific Council of the Institute of Computer Science of the Polish Academy of Sciences, guiding its works as Chairperson in 1972-1983. Last but not least, in recent years she greatly contributed to the foundation of the Polish Society of Logic and Philosophy of Science.

No description of Rasiowa's activities would be complete without a mention of her deep involvement in the development of research journals she was involved with. The most cherished by her, *Fundamenta Informaticae*, had
been established in 1977 mostly due to her efforts, and Helena Rasiowa was its Editor-in-Chief until her death. Even when her illness began to take overtake her she never ceased to control the preparation of the consecutive issues of the journal. In particular, she acted as Editor of a special anniversary issue commemorating the publication of the 20th volume of FI in 1994. Moreover, demonstrating once more proof of her inexhaustible energy, she was an active Collecting Editor with *Studia Logica* (since 1974) and Associate Editor with the *Journal of Approximate Reasoning* since 1986.

Professor Rasiowa educated generations of students and researchers, in particular, she had supervised over 20 Ph.D. theses. Her lectures were known all over the world. She had been a visiting professor at 14 universities, ranging from Bahia Blanca in Argentina to Moscow in the Soviet Union. passing through Campinas in Brasil, UNAM in Mexico, Rome in Italy and Oxford University in England. In the USA she was hosted by universities such as Princeton, University of Chicago, University of California at Berkeley and the University of North Carolina at Charlotte. Moreover, she gave invited lectures at 46 universities and research establishments abroad, in some of them more than once.

She contributed to mathematical literature with three important books and more than 100 publications. The topics covered by her work include proof theory and deductive logic, algebraic methods in logic and algebras related to logics, classical and non-classical logics, algorithmic and approximation logics, and artificial intelligence. She worked on a new monograph till her very last days. The intended title was *Algebraic Analysis of Non-Classical First Order Logics.*

The study of the relationship between logic and algebra, originated by the work of George Boole and continued by A. Lindenbaum, A. Tarski, M.H. Stone, R. McKinsey, A. Mostowski and L. Henkin – to mention only a few – was the main research subject of Helena Rasiowa. One of the crucial moments in the development of algebraic study of logic was the introduction of Lindenbaums and Tarski's method for treating equivalence classes of formulas as elements of an abstract algebraic system. This provided a link between theories based on classical logic and Boolean algebras. An analogous correspondence between intuitionistic logic and pseudo-complemented lattices was established by Stone and Tarski, while the application of algebraic methods to modal logics was originated by McKinsey and Tarski (1944-1948). Another important idea leading to the emergence of the field of algebraic logic was the treatment of formulas as algebraic functions in certain algebras, initiated by Lukasiewicz and Post with their generalization of truth tables.

Helena Rasiowa became very active in these areas in the early fifties. Her research work on algebraic logic was aimed at finding a precise description for the mathematical structure of formalised logical systems. Her early papers contain several examples of algebras associated with logical systems as well as algebraic proofs of some of their properties. Jointly with Roman Sikorski she presented the first algebraic proof of the Gödel completeness theorem for classical predicate logic. Next, she algebraically proved analogous theorems for intuitionistic and modal logics. In other papers she turned to other nonclassical logics, applying with success the algebraic tools she had developed. All these investigations led her to a synthesis of the results hitherto obtained; she developed a general framework for an algebraic presentation of propositional and first order logics. In particular, she established elegant formal techniques for associating classes of algebras with logical systems and for providing their algebraic semantics.

Helena Rasiowa greatly contributed to the development of research in Poland on applications of logical methods in the foundations of computer science. She was one of the first to realize the great importance of mathematical logic for computer science - and at the same time she clearly saw the significance of computer science for the development of logic itself. In the last 20 years of her scientific activity she focused her efforts on the realization of this main idea through papers, seminars and research projects. Many of her students and collaborators who attended her lectures or seminars, those who wrote their PhD theses under her supervision, are now continuing the work she initiated. There remains no doubt today that she was right in the appreciation of the significance of the field. Among the authors of important research results on logical and algebraic methods in computer science the names of her students can be found quite often. Moreover, some of these important results have appeared in a journal which would not have existed without her dedication and to which she had been Editor-in-Chief for man years, i.e. *Fundamenta Informaticae*.

The form of this short article makes difficult a complete presentation of her achievements in the field of applications of logical and algebraic methods in computer science. She was the author of more then 30 papers, two lecture notes, and an unfinished monograph in which she relates algebraic methods of non-classical logics with applications in the foundations of computer science. She was able to write eight chapters before she was taken to the hospital.

Her contribution to theoretical computer science stems from her conviction that there are deep relations between methods of algebra and logic on one side and essential problems of foundations of computer science on the other. Among these problems she clearly distinguished inference methods characteristic of computer science and its applications. This conviction of hers had been supported by her results on many-valued and nonclassical logics, especially on applications of various generalizations of Post algebras to logics of programs and approximation logics.

Note: One book written by Helena Rasiowa was *Introduction to Modern Mathematics*, written in 1971 and published in an English translation in 1973.

- Fitting, Melvin. "A Tribute to Professor Helena Rasiowa," http://comet.lehman.cuny.edu/fitting/bookspapers/pdf/papers/Rasiowa.pdf
- Font, Joseph. "On the contributions of Helena Rasiowa to mathematical logic," Multiple-Valued Logic, Vol. 4 (1999), 159-179
- MathSciNet [subscription required]
- Author Profile at zbMath
- Mathematics Genealogy Project
- Biography at the MacTutor History of Mathematics Archive