Tarski’s influence on computer science.

*(English)*Zbl 1425.03003
Garrido, Ángel (ed.) et al., The Lvov-Warsaw school. Past and present. Cham: Birkhäuser. Stud. Univers. Log., 391-404 (2018).

This is an interesting contribution to the history of the relations between logic and computer sciences by one of the major logicians of the 20th century. This paper builds on and completes the biography of Alfred Tarski co-written by the author and his wife, Anita Feferman. The central question of the paper is the following:

“Tarski became recognized as one of the most important logicians of the twentieth century through his many contributions to the areas of set theory, model theory, the semantics of formal languages, decidable theories and decision procedures, undecidable theories, universal algebra, axiomatics of geometry, and algebraic logic. What, in all that, are the connections with computer science?”

After recalling Tarski’s pioneering figure as a logician in the US, the article indicates a month-long Summer Institute in Symbolic Logic held at Cornell University in 1957 as a turning point for this story: “the first to include many speakers from the emerging field of computer science, the theoretical foundations of which had been laid in the 1930s by Gödel, Church, Turing, Post, and Kleene.”

Some of Tarski’s prior students, present at the meeting, worked into the practical applications of one of Tarski’s major results, namely his decision procedure for the algebra of real numbers, and in this way they helped disseminating the knowledge of Tarski’s logical works among computer scientists. Around the same years, companies such as IBM employed researchers with background in mathematics and logic, some of whom had also attended the 1957 memorable meeting.

Another episode crediting the importance of Tarski for the development of computer science regards the vicissitudes related to the publication of his paper The completeness of elementary algebra and geometry. Unable to publish this paper in Paris in 1940, because of the II world war, Tarski revised and published it years later as a RAND report under the title: A decision procedure for elementary algebra and geometry (1948). The RAND corporation was chiefly interested in applying Tarski’s decision method to game theory, and this practical interest for decidability explains the change in the title of the paper.

Even if Tarski had not a high opinion for his students who took a career in computer science, he nevertheless made an effort to reformulate his results in a language more digestible to mathematicians. This can also explain the circulation of his results within mathematicians and then among computer scientists.

On these grounds the author can conclude: “In whatever way the claim is formulated, I think it is fair to say that Tarski’s ideas and the approaches he promoted are so pervasive that even if his influence in this and the various other areas of computer science about which I spoke was not direct it was there at the base, and – to mix a metaphor – it was there in the air, and so the nature and importance of his influence eminently deserves to be recognized.”

Besides being in its own an informative piece in the history of 20th century logic, this article could be also taken as a starting point for further works in the sociology of logic and computer sciences.

For the entire collection see [Zbl 1403.01005].

“Tarski became recognized as one of the most important logicians of the twentieth century through his many contributions to the areas of set theory, model theory, the semantics of formal languages, decidable theories and decision procedures, undecidable theories, universal algebra, axiomatics of geometry, and algebraic logic. What, in all that, are the connections with computer science?”

After recalling Tarski’s pioneering figure as a logician in the US, the article indicates a month-long Summer Institute in Symbolic Logic held at Cornell University in 1957 as a turning point for this story: “the first to include many speakers from the emerging field of computer science, the theoretical foundations of which had been laid in the 1930s by Gödel, Church, Turing, Post, and Kleene.”

Some of Tarski’s prior students, present at the meeting, worked into the practical applications of one of Tarski’s major results, namely his decision procedure for the algebra of real numbers, and in this way they helped disseminating the knowledge of Tarski’s logical works among computer scientists. Around the same years, companies such as IBM employed researchers with background in mathematics and logic, some of whom had also attended the 1957 memorable meeting.

Another episode crediting the importance of Tarski for the development of computer science regards the vicissitudes related to the publication of his paper The completeness of elementary algebra and geometry. Unable to publish this paper in Paris in 1940, because of the II world war, Tarski revised and published it years later as a RAND report under the title: A decision procedure for elementary algebra and geometry (1948). The RAND corporation was chiefly interested in applying Tarski’s decision method to game theory, and this practical interest for decidability explains the change in the title of the paper.

Even if Tarski had not a high opinion for his students who took a career in computer science, he nevertheless made an effort to reformulate his results in a language more digestible to mathematicians. This can also explain the circulation of his results within mathematicians and then among computer scientists.

On these grounds the author can conclude: “In whatever way the claim is formulated, I think it is fair to say that Tarski’s ideas and the approaches he promoted are so pervasive that even if his influence in this and the various other areas of computer science about which I spoke was not direct it was there at the base, and – to mix a metaphor – it was there in the air, and so the nature and importance of his influence eminently deserves to be recognized.”

Besides being in its own an informative piece in the history of 20th century logic, this article could be also taken as a starting point for further works in the sociology of logic and computer sciences.

For the entire collection see [Zbl 1403.01005].

Reviewer: Davide Crippa (Paris)

##### MSC:

03-03 | History of mathematical logic and foundations |

68-03 | History of computer science |

01A70 | Biographies, obituaries, personalia, bibliographies |

##### Biographic References:

Tarski, Alfred##### Software:

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\textit{S. Feferman}, in: The Lvov-Warsaw school. Past and present. Cham: Birkhäuser. 391--404 (2018; Zbl 1425.03003)

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