Dana Scott

Dana Stewart Scott
Born	1932
Awards	ACM Turing Award 1976, Tarski lectures 1989
Scientific career
Fields	Computer Science Mathematics Philosophy
Institutions	University of California, Berkeley Oxford University Carnegie Mellon University

Dana Stewart Scott (born 1932) is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California. His research career has spanned computer science, mathematics, and philosophy, and has been characterized by a marriage of a concern for elucidating fundamental concepts in the manner of informal rigor, with a cultivation of mathematically hard problems that bear on these concepts. His work on automata theory earned him the ACM Turing Award in 1976, while his collaborative work with Christopher Strachey in the 1970s laid the foundations of modern approaches to the semantics of programming languages. He has worked also on modal logic, topology, and category theory. He is the editor-in-chief of the new journal Logical Methods in Computer Science.

Early career

He received his BA in Mathematics from the University of California, Berkeley in 1954.

He wrote his Ph.D. thesis on Convergent Sequences of Complete Theories under the supervision of Alonzo Church while at Princeton, and defended his thesis in 1958. After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960.

In 1959, he published a joint paper with Michael O. Rabin, a colleague from Princeton, entitled Finite Automata and Their Decision Problem, which introduced the idea of nondeterministic machines to automata theory. This work led to the joint bestowal of the Turing Award on the two, for the introduction of this fundamental concept of computational complexity theory.

University of California, Berkeley, 1960–1963

Scott took up a post as Assistant Professor of Mathematics, at the University of California, Berkeley, the university of Alfred Tarski, and involved himself with classical issues in mathematical logic, especially set theory and Tarskian model theory.

During this period he started supervising Ph.D. students, such as James Halpern (Contributions to the Study of the Independence of the Axiom of Choice) and Edgar Lopez-Escobar (Infinitely Long Formulas with Countable Quantifier Degrees). Scott's work as research supervisor has been an important source of his intellectual influence.

Modal logic

Scott also began working on modal logic in this period, beginning a collaboration with John Lemmon, who moved to Claremont, California in 1963. Scott was especially interested in tense logic and the connection to the treatment of time in natural-language semantics, and began collaborating with Richard Montague (Copeland 2004). Later, Scott and Montague were independently to discover an important generalisation of Kripke semantics for modal and tense logic called Scott-Montague semantics (Scott 1970).

John Lemmon and Scott began work on a modal-logic textbook that was interrupted by Lemmon's death in 1966. Scott circulated the incomplete monograph amongst colleagues, introducing a number of important techniques in the semantics of model theory, most importantly presenting a refinement of canonical model that became standard, and introducing the technique of constructing models through filtrations, both of which are core concepts in modern Kripke semantics (Blackburn, de Rijke, and Venema, 2001). Scott eventually published the work as An Introduction to Modal Logic (Lemmon and Scott, 1977).

Stanford, Amsterdam and Princeton, 1963–1972

Following an initial observation of Robert Solovay, Scott formulated the concept of Boolean-valued model (Solovay and Petr Vopěnka did likewise at around the same time). In 1967 Scott published a paper, A Proof of the Independence of the Continuum Hypothesis, in which he used Boolean-valued models to provide an alternate analysis of the independence of the continuum hypothesis to that provided by Paul Cohen. This work led to the award of the Leroy P. Steele Prize in 1972.

Oxford University, 1972–1981

Dana Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of Oxford University in 1972.

Semantics of programming languages

This period saw Scott working closely with Christopher Strachey, and the two managed, despite intense administrative pressures, to oversee a great deal of fundamental work on providing a mathematical foundation for the semantics of programming languages, the work for which Scott is best known. Together, their work constitutes the Scott-Strachey approach to denotational semantics, and it constitutes one of the most influential pieces of work in theoretical computer science, and can perhaps be regarded as founding one of the major schools of computer science. One of Scott's largest contributions is his formulation of domain theory, allowing programs involving recursive functions and looping-control constructs to be given a denotational semantics. Additionally, he provided a foundation for the understanding of infinitary and continuous information through domain theory and his theory of information systems.

Scott's work of this period led to the bestowal of:

• The 1990 Harold Pender Award for his application of concepts from logic and algebra to the development of mathematical semantics of programming languages;
• The 1997 Rolf Schock Prize in logic and philosophy from the Royal Swedish Academy of Sciences for his conceptually oriented logical works, especially the creation of domain theory, which has made it possible to extend Tarski's semantical paradigm to programming languages as well as to construct models of Curry's combinatory logic and Church's calculus of lambda conversion; and
• The 2001 Bolzano Prize for Merit in the Mathematical Sciences by the Czech Academy of Sciences.

Carnegie Mellon University 1981–2003

At Carnegie Mellon University, Scott proposed the theory of equilogical spaces as a generalization of domain theory. In 1994 he was inducted as a Fellow of the Association for Computing Machinery.

References

Works by Scott

• With Michael O. Rabin, 1959. Finite Automata and Their Decision Problem.
• 1967. A proof of the independence of the continuum hypothesis. Mathematical Systems Theory 1:89-111.
• 1970. 'Advice in modal logic'. In Philosophical Problems in Logic, ed. K. Lambert, pages 143-173.
• With John Lemmon, 1977. An Introduction to Modal Logic. Oxford: Blackwell.

Other works

• Blackburn, de Rijke and Venema, 2001. Modal logic. Cambridge University Press.
• Jack Copeland, 2004. Arthur Prior. In the Stanford Encyclopedia of Philosophy.
• Joseph E. Stoy, Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory, MIT Press, 1977. ISBN 0-262-19147-4

External links

• Dana S. Scott's home page
• DOMAIN 2002 Workshop on Domain Theory – held in honor of Scott's 70th birthday.
• Dana Scott at the Mathematics Genealogy Project