Editing Dana Scott

{{short description|American logician (born 1932)}}
{{more footnotes|date=February 2018}}
{{Infobox scientist
| name              = Dana Stewart Scott
| image             = Scott Dana small.jpg
| caption           = 
| birth_date        = {{birth date and age|1932|10|11}}
| birth_place       = [[Berkeley, California]]
| death_date        = 
| death_place       = 
| nationality       = 
| field             =
{{plainlist|
* [[Computer science]]
* [[Mathematics]]
* [[Philosophy]]
}}
| work_institution  =
{{plainlist|
* [[University of Chicago]]
* [[University of California, Berkeley]]
* [[Stanford]]
* [[Merton College, Oxford]]
* [[Carnegie Mellon University]]
}}
| education         = [[University of California, Berkeley]] ([[Bachelor of Arts|BA]])<br>[[Princeton University]] ([[Master of Arts|MA]], [[Doctor of Philosophy|PhD]])
| doctoral_advisor  = [[Alonzo Church]]
| doctoral_students =
{{plainlist|
* [[Jack Copeland]]
* [[Michael Fourman]]
* [[Kenneth Kunen]]
* [[Angus Macintyre]]
* [[Peter Mosses]]
* [[Ketan Mulmuley]]
* [[Marko Petkovšek]]
* [[Fred S. Roberts]]
* [[Krister Segerberg]]
* [[David Turner (computer scientist)|David Turner]]
* [[Martin Davies (philosopher)|Martin Davies]]
}}
| thesis_title      = Convergent Sequences of Complete Theories
| thesis_url        = https://www.worldcat.org/oclc/83498680
| thesis_year       = 1958
| known_for         =
{{plainlist|
* [[Automata theory]]
* [[Cartesian monoid]]
* [[Logic of Computable Functions]]
* [[Semantics of programming languages]]
* [[Modal μ-calculus]]
* [[Nondeterministic finite automaton]]
* [[Scott domain]]
* [[Mogensen–Scott encoding|Scott encoding]]
* [[Scott information system]]
* [[Scott continuity|Scott topology]]
* [[Scott's trick]]
* [[Scott-Montague semantics]]
* [[Scott–Potter set theory]]
* [[Denotational semantics|Scott–Strachey semantics]]
* [[Powerset construction|Rabin–Scott powerset construction]]
}}
| prizes            =
{{plainlist|
* [[Leroy P. Steele Prize]] {{small|(1972)}}
* [[Turing Award]] {{small|(1976)}}
* [[Tarski Lectures]] {{small|(1989)}}
* [[Harold Pender Award]] {{small|(1990)}}
* [[Gödel Lecture]] {{small|(1991)}}
* [[Rolf Schock Prizes|Rolf Schock Prize]] (Logic and Philosophy) {{small|(1997)}}
}}
}}
'''Dana Stewart Scott''' (born October 11, 1932) is an American logician who is the emeritus [[Named chair|Hillman University Professor]] of [[computer science|Computer Science]], [[Philosophy]], and [[mathematical logic|Mathematical Logic]] at [[Carnegie Mellon University]];<ref>{{cite web|url=https://www.cmu.edu/math/people/faculty/scott.html|title=Dana S. Scott|accessdate=13 October 2024}}</ref> he is now retired and lives in [[Berkeley, California]]. His work on [[automata theory]] earned him the [[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 also worked on [[modal logic]], [[topology]], and [[category theory]].

==Early career==
He received his [[Bachelor of Arts|B.A.]] in Mathematics from the [[University of California, Berkeley]], in 1954. He wrote his [[Doctor of Philosophy|Ph.D. thesis]] on ''Convergent Sequences of Complete Theories'' under the supervision of [[Alonzo Church]] while at [[Princeton University|Princeton]], and defended his thesis in 1958. [[Solomon Feferman]] (2005) writes of this period:

{{quote|''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 with [[Alfred Tarski|Tarski]] and became part of the group that surrounded him, including me and [[Richard 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.<ref>Feferman & Feferman 2004.</ref>  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 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, titled ''Finite Automata and Their Decision Problem'' (Scott and Rabin 1959) 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, back at the [[University of California, Berkeley]], and involved himself with classical issues in [[mathematical logic]], especially [[set theory]] and Tarskian [[model theory]]. He proved that the [[axiom of constructibility]] is incompatible with the existence of a [[measurable cardinal]], a result considered ''seminal'' in the evolution of set theory.<ref> Kanamori, The Higher infinite, p. 44, 49.</ref>

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'').

===Modal and tense 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 [[Arthur Prior]]'s approach to [[tense logic]] and the connection to the treatment of time in natural-language semantics, and began collaborating with [[Richard Montague]] (Copeland 2004), whom he had known from his days as an undergraduate at Berkeley.  Later, Scott and Montague independently discovered 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 the ''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 & Scott, 1977).

==Stanford, Amsterdam and Princeton, 1963–1972==
Following an initial observation of [[Robert Solovay]], Scott formulated the concept of [[Boolean-valued model]], as 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 (mathematician)|Paul Cohen]]. This work led to the award of the [[Leroy P. Steele Prize]] in 1972.

==University of Oxford, 1972–1981==
Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of the [[University of Oxford]] in 1972. He was member of [[Merton College, Oxford|Merton College]] while at Oxford and is now an Honorary Fellow of the college.

===Semantics of programming languages===
This period saw Scott working with [[Christopher Strachey]], and the two
managed, despite administrative pressures,{{Clarify|reason=vague|date=May 2017}} to do work on providing a mathematical foundation for the semantics of programming languages, the work for which Scott is best known{{opinion|date=January 2016}}. Together, their work constitutes the Scott–Strachey approach to [[denotational semantics]], an important and seminal contribution to [[theoretical computer science]]. One of Scott's contributions is his formulation of [[domain 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 of [[Scott information system|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 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 2001 [[Bolzano Prize]] for Merit in the Mathematical Sciences by the [[Czech Academy of Sciences]]
* The 2007 [[EATCS]] Award for his contribution to theoretical computer science.

==Carnegie Mellon University, 1981–2003==
At [[Carnegie Mellon University]], Scott proposed the theory of [[equilogical spaces]] as a successor theory to domain theory; among its many advantages, the category of equilogical spaces is a [[cartesian closed category]], whereas the category of domains<ref>Where here Dana Scott counts the category of domains to be the category whose objects are pointed directed-[[complete partial order]]s (DCPOs), and whose morphisms are the strict, [[Scott-continuous]] functions</ref> is not. In 1994, he was inducted as a [[Fellow]] of the [[Association for Computing Machinery]]. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-07-14.</ref>

==Bibliography==
* With [[Michael 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 on modal logic'.  In ''Philosophical Problems in Logic'', ed. K. Lambert, pages 143–173.
* With [[John Lemmon]], 1977.  ''An Introduction to Modal Logic''. Oxford: Blackwell.
* {{cite book |last1=Gierz |first1=G. |last2=Hofmann |first2=K. H. |last3=Keimel |first3=K. |last4=Lawson |first4=J. D. |last5=Mislove |first5=M. W. |last6=Scott |first6=D. S. |title=Continuous Lattices and Domains |volume=93 |series=Encyclopedia of Mathematics and its Applications |publisher=Cambridge University Press |year=2003 |isbn=978-0521803380 |url-access=registration |url=https://archive.org/details/continuouslattic0000unse }}

==References==
{{reflist}}

==Further reading==
*Blackburn, de Rijke and Venema (2001). [https://books.google.com/books/about/Modal_Logic.html?id=pbb_Asgoq0oC ''Modal logic'']. [[Cambridge University Press]].
*[[Jack Copeland]] (2004). [http://plato.stanford.edu/entries/prior/ Arthur Prior].  In the [[Stanford Encyclopedia of Philosophy]].
*[[Anita Burdman Feferman]] and [[Solomon Feferman]] (2004).  [http://google.com/books?id=wqktlxHo9wkC ''Alfred Tarski: life and logic'']. Cambridge University Press, {{ISBN|0-521-80240-7}}, {{ISBN|978-0-521-80240-6}}.
*[[Solomon Feferman]] (2005). [http://math.stanford.edu/~feferman/papers/tarskiandcs.pdf Tarski's influence on computer science].  Proc. LICS'05. [[IEEE Press]].
*Joseph E. Stoy (1977). ''Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory''. [[MIT Press]]. {{ISBN|0-262-19147-4}}

==External links==
* {{official website|http://www-2.cs.cmu.edu/~scott/}} 
* ''[https://web.archive.org/web/20041012130754/http://floc02.diku.dk/DOMAIN/ DOMAIN 2002 Workshop on Domain Theory]''  — held in honor of Scott's 70th birthday.
* {{MathGenealogy|id=8024}}
* {{AcademicSearch|824300}}
* Dana Scott interviewed by [[Gordon Plotkin]], as part of the [[Association for Computing Machinery]] series of interviews of Turing award winners: [https://www.youtube.com/watch?v=OHHmuU_eRg0 Part 1 (Nov 12, 2020)] [https://www.youtube.com/watch?v=M2yXOfwo-vc Part 2 (Dec 29, 2020)] [https://www.youtube.com/watch?v=l_wyFxwkZJc Part 3 (Jan 12, 2021)] [https://www.youtube.com/watch?v=E31qtmAuaVU Part 4 (Feb 18, 2021)]
* ''[https://github.com/CMU-HoTT/scott/ Selected papers of Dana S. Scott]''

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{{succession box | before=[[Jerzy Łoś]]| title=President of the [[DLMPST|DLMPST/IUHPST]] | years=1983&ndash;1987 | after=[[Laurence Jonathan Cohen]]}}
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{{DEFAULTSORT:Scott, Dana}}
[[Category:American computer scientists]]
[[Category:American logicians]]
[[Category:1932 births]]
[[Category:Living people]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Carnegie Mellon University faculty]]
[[Category:1994 fellows of the Association for Computing Machinery]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of Merton College, Oxford]]
[[Category:Formal methods people]]
[[Category:Lattice theorists]]
[[Category:Mathematical logicians]]
[[Category:Modal logicians]]
[[Category:Model theorists]]
[[Category:Programming language researchers]]
[[Category:Rolf Schock Prize laureates]]
[[Category:Semanticists]]
[[Category:Set theorists]]
[[Category:American topologists]]
[[Category:Turing Award laureates]]
[[Category:University of Chicago faculty]]
[[Category:University of California, Berkeley College of Letters and Science faculty]]
[[Category:Princeton University alumni]]
[[Category:UC Berkeley College of Letters and Science alumni]]
[[Category:People from Berkeley, California]]
[[Category:Engineers from California]]
[[Category:Scientists from California]]
[[Category:20th-century American mathematicians]]
[[Category:20th-century American engineers]]
[[Category:21st-century American engineers]]
[[Category:20th-century American scientists]]
[[Category:21st-century American scientists]]
[[Category:21st-century American mathematicians]]