Jump to content

Dana Scott

From Wikipedia, the free encyclopedia
(Redirected fromDana S. Scott)
Dana Stewart Scott
Born(1932-10-11)October 11, 1932(age 91)
EducationUC Berkeley(B.A., 1954)Princeton University(Ph.D., 1958)
Known for
Awards
Scientific career
Fields
Institutions
ThesisConvergent Sequences of Complete Theories(1958)
Doctoral advisorAlonzo Church
Doctoral students

Dana Stewart Scott(born October 11, 1932) is an American logician who is the emeritus Hillman University Professor ofComputer Science,Philosophy,andMathematical LogicatCarnegie Mellon University;he is now retired and lives inBerkeley, California.His work onautomata theoryearned him theTuring Awardin 1976, while his collaborative work withChristopher Stracheyin the 1970s laid the foundations of modern approaches to thesemantics of programming languages.He has also worked onmodal logic,topology,andcategory theory.

Early career

[edit]

He received hisB.A.in Mathematics from theUniversity of California, Berkeley,in 1954. He wrote hisPh.D. thesisonConvergent Sequences of Complete Theoriesunder the supervision ofAlonzo Churchwhile atPrinceton,and defended his thesis in 1958.Solomon Feferman(2005) writes of this period:

Scott began his studies in logic at Berkeley in the early 50s while still an undergraduate. His unusual abilities were soon recognized and he quickly moved on to graduate classes and seminars withTarskiand became part of the group that surrounded him, including me andRichard Montague;so it was at that time that we became friends. Scott was clearly in line to do a Ph. D. with Tarski, but they had a falling out for reasons explained in our biography.[1]Upset by that, Scott left for Princeton where he finished with a Ph. D. under Alonzo Church. But it was not long before the relationship between them was mended to the point that Tarski could say to him, "I hope I can call you my student."

After completing his Ph.D. studies, he moved to theUniversity of Chicago,working as an instructor there until 1960. In 1959, he published a joint paper withMichael O. Rabin,a colleague from Princeton, titledFinite Automata and Their Decision Problem(Scott and Rabin 1959) which introduced the idea of nondeterministic machines toautomata theory.This work led to the joint bestowal of theTuring Awardon the two, for the introduction of this fundamental concept ofcomputational complexity theory.

University of California, Berkeley, 1960–1963

[edit]

Scott took up a post as Assistant Professor of Mathematics, back at theUniversity of California, Berkeley,and involved himself with classical issues inmathematical logic,especiallyset theoryand Tarskianmodel theory.He proved that theaxiom of constructibilityis incompatible with the existence of ameasurable cardinal,a result consideredseminalin the evolution of set theory.[2]

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).

[edit]

Scott also began working onmodal logicin this period, beginning a collaboration withJohn Lemmon,who moved toClaremont, California,in 1963. Scott was especially interested inArthur Prior's approach totense logicand the connection to the treatment of time in natural-language semantics, and began collaborating withRichard Montague(Copeland 2004), whom he had known from his days as an undergraduate at Berkeley. Later, Scott and Montague independently discovered an important generalisation ofKripke semanticsfor modal and tense logic, calledScott-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 ofcanonical modelthat became standard, and introducing the technique of constructing models throughfiltrations,both of which are core concepts in modern Kripke semantics (Blackburn, de Rijke, and Venema, 2001). Scott eventually published the work asAn Introduction to Modal Logic(Lemmon & Scott, 1977).

Stanford, Amsterdam and Princeton, 1963–1972

[edit]

Following an initial observation ofRobert Solovay,Scott formulated the concept ofBoolean-valued model,as Solovay andPetr Vopěnkadid 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 thecontinuum hypothesisto that provided byPaul Cohen.This work led to the award of theLeroy P. Steele Prizein 1972.

University of Oxford, 1972–1981

[edit]

Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of theUniversity of Oxfordin 1972. He was member ofMerton Collegewhile at Oxford and is now an Honorary Fellow of the college.

Semantics of programming languages

[edit]

This period saw Scott working withChristopher Strachey,and the two managed, despite administrative pressures,[clarification needed]to do work on providing a mathematical foundation for the semantics of programming languages, the work for which Scott is best known[opinion].Together, their work constitutes the Scott–Strachey approach todenotational semantics,an important and seminal contribution totheoretical computer science.One of Scott's contributions is his formulation ofdomain theory,allowing programs involving recursive functions and looping-control constructs to be given denotational semantics. Additionally, he provided a foundation for the understanding of infinitary and continuous information through domain theory and his theory ofinformation systems.

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

  • The 1990Harold Pender Awardfor hisapplication of concepts from logic and algebra to the development of mathematical semantics of programming languages;
  • The 1997Rolf Schock Prizein logic and philosophy from theRoyal Swedish Academy of Sciencesforhis conceptually oriented logical works, especially the creation of domain theory, which has made it possible to extend Tarski's semantic paradigm to programming languages as well as to construct models of Curry's combinatory logic and Church's calculus of lambda conversion;and
  • The 2001Bolzano Prizefor Merit in the Mathematical Sciences by theCzech Academy of Sciences
  • The 2007EATCSAward for his contribution to theoretical computer science.

Carnegie Mellon University, 1981–2003

[edit]

AtCarnegie Mellon University,Scott proposed the theory ofequilogical spacesas a successor theory to domain theory; among its many advantages, the category of equilogical spaces is acartesian closed category,whereas the category of domains[3]is not. In 1994, he was inducted as aFellowof theAssociation for Computing Machinery.In 2012 he became a fellow of theAmerican Mathematical Society.[4]

Bibliography

[edit]
  • WithMichael O. Rabin,1959.Finite Automata and Their Decision Problem.doi:10.1147/rd.32.0114
  • 1967.A proof of the independence of the continuum hypothesis.Mathematical Systems Theory 1:89–111.
  • 1970. 'Advice in modal logic'. InPhilosophical Problems in Logic,ed. K. Lambert, pages 143–173.
  • WithJohn Lemmon,1977.An Introduction to Modal Logic.Oxford: Blackwell.
  • Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M. W.; Scott, D. S. (2003).Continuous Lattices and Domains.Encyclopedia of Mathematics and its Applications. Vol. 93. Cambridge University Press.ISBN978-0521803380.

References

[edit]
  1. ^Feferman & Feferman 2004.
  2. ^Kanamori, The Higher infinite, p. 44, 49.
  3. ^Where here Dana Scott counts the category of domains to be the category whose objects are pointed directed-complete partial orders(DCPOs), and whose morphisms are the strict,Scott-continuousfunctions
  4. ^List of Fellows of the American Mathematical Society,retrieved 2013-07-14.

Further reading

[edit]
[edit]
Academic offices
Preceded by President of theDLMPST/IUHPST
1983–1987
Succeeded by