**Jan Kalicki** was a Polish mathematician who worked on logical matrices and equational logic.

- During the summer of 1939 as Kalicki waited to begin his university education, Europe moved closer to war.
- It was in these extraordinarily difficult conditions that Kalicki received his university education, studying mathematics and philosophy.
- Kalicki survived and after the war ended in 1945 he was awarded an M.A. in both philosophy and mathematics.
- Financed by a British Council Scholarship for two years, Kalicki studied at the University of London, receiving his doctorate in mathematical logic in July 1948.
- By the time Kalicki was awarded his doctorate Poland was a communist controlled country which Kalicki felt would not encourage free thinking academic studies.
- Kalicki worked on logical matrices and equational logic and published 13 papers on these topics from 1948 until his death five years later.
- In On Tarski's matrix method (1948), Kalicki defines the sum , the product and also a partial ordering of logical matrices.
- Corresponding to each truth table MMM, Kalicki considers the set of all formulae formed from variables and the connective DDD, which are tautologies for MMM.
- Kalicki defines relations of isomorphism, equivalence, and inclusion of truth tables.
- The next paper in the same part of the Journal of Symbolic Logic is also by Kalicki.
- It is A test for the existence of tautologies according to many-valued truth-tables in which Kalicki gives an effective procedure to decide whether the set of tautologies determined by a given truth table with a finite number of truth-values is empty.
- Two years later another paper by Kalicki in the Journal of Symbolic Logic is A test for the equality of truth-tables which gives a necessary and sufficient condition for the equivalence of two truth-tables.
- However for the problem of deciding whether two infinite-valued truth-tables are equal is unsolvable as Kalicki showed in a paper which was not published until 1954 after his death.
- Kalicki's first appointment at the University of California was as Visiting Assistant Professor of Mathematics at Berkeley where Tarski was working, but after one year he obtained a permanent appointment as Assistant Professor of Mathematics at the Davis campus.
- He had unbounded confidence that almost anybody could be brought to an understanding of the fundamental results of modern logic if only he, Kalicki, could find the right words.
- Kalicki had remarkable success with the type of students who consider themselves hopelessly incapable of mastering things mathematical.

Born 28 January 1922, Warsaw, Poland. Died 25 November 1953, Contra Costa County, USA.

View full biography at MacTutor

Origin Poland

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive