Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of

Computer Science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

Philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

, and

Mathematical Logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

; he is now retired and lives in

Berkeley, California Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emer ...

. His work on

automata theory Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

earned him the

Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...

in 1976, while his collaborative work with

Christopher Strachey Christopher S. Strachey (; 16 November 1916 – 18 May 1975) was a British computer scientist. He was one of the founders of denotational semantics, and a pioneer in programming language design and computer time-sharing.F. J. Corbató, et al. ...

in the 1970s laid the foundations of modern approaches to the

semantics of programming languages In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid string (computer science), strings in a programming language syntax. Semantic ...

. He has worked also on modal logic,

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

, and

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

Early career

He received his

B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

in Mathematics from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, in 1954. He wrote his Ph.D. thesis on ''Convergent Sequences of Complete Theories'' under the supervision of

Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scien ...

while at

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

, and defended his thesis in 1958.

Solomon Feferman Solomon Feferman (December 13, 1928 – July 26, 2016) was an American philosopher and mathematician who worked in mathematical logic. Life Solomon Feferman was born in The Bronx in New York City to working-class parents who had immigrated to th ...

(2005) writes of this period: After completing his Ph.D. studies, he moved to the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, working as an instructor there until 1960. In 1959, he published a joint paper with

Michael O. Rabin Michael Oser Rabin ( he, מִיכָאֵל עוזר רַבִּין; born September 1, 1931) is an Israeli mathematician and computer scientist and a recipient of the Turing Award. Biography Early life and education Rabin was born in 1931 in ...

, a colleague from Princeton, titled ''Finite Automata and Their Decision Problem'' (Scott and Rabin 1959) which introduced the idea of nondeterministic machines to

. This work led to the joint bestowal of the

on the two, for the introduction of this fundamental concept of

computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by ...

University of California, Berkeley, 1960–1963

Scott took up a post as Assistant Professor of Mathematics, back at the

, and involved himself with classical issues in

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

, especially

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

and Tarskian

model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

. 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 Edward John Lemmon (1 June 1930 – 29 July 1966) was a British logician and philosopher born in Sheffield, England. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously (Lemm ...

, who moved to Claremont, California, in 1963. Scott was especially interested in

Arthur Prior Arthur Norman Prior (4 December 1914 – 6 October 1969), usually cited as A. N. Prior, was a New Zealand–born logician and philosopher. Prior (1957) founded tense logic, now also known as temporal logic, and made important contribution ...

's approach to

tense logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

and the connection to the treatment of time in natural-language semantics, and began collaborating with

Richard Montague Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher who made contributions to mathematical logic and the philosophy of language. He is known for proposing Montague grammar to formalize ...

(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 Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Jo ...

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 & Scott, 1977).

Stanford, Amsterdam and Princeton, 1963–1972

Following an initial observation of

Robert Solovay Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory. Biography Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on ' ...

, Scott formulated the concept of

Boolean-valued model In mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not limited to "true" and "false", but instead take v ...

, as Solovay and

Petr Vopěnka Petr Vopěnka (16 May 1935 – 20 March 2015) was a Czech mathematician. In the early seventies, he developed alternative set theory (i.e. alternative to the classical Cantor theory), which he subsequently developed in a series of articles and m ...

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 In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...

to that provided by

Paul Cohen Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician. He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was award ...

. This work led to the award of the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

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 , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

in 1972. He was member of

Merton College Merton College (in full: The House or College of Scholars of Merton in the University of Oxford) is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, ch ...

while at Oxford and is now an Honorary Fellow of the college.

Semantics of programming languages

This period saw Scott working with

, and the two managed, despite administrative pressures, to do 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, an important and seminal contribution to

theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...

. One of Scott's contributions is his formulation of

domain theory Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer ...

, 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

information systems An information system (IS) is a formal, sociotechnical, organizational system designed to collect, process, information storage, store, and information distribution, distribute information. From a sociotechnical perspective, information systems a ...

. Scott's work of this period led to the bestowal of: * The 1990

Harold Pender Award The Harold Pender Award, initiated in 1972 and named after founding Dean Harold Pender, is given by the Faculty of the School of Engineering and Applied Science of the University of Pennsylvania to an outstanding member of the engineering professi ...

for his ''application of concepts from logic and algebra to the development of mathematical semantics of programming languages''; * The 1997

Rolf Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and, since 2005, are awarded every three years. Each recipient current ...

in logic and philosophy from the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special ...

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 Czech Academy of Sciences (abbr. CAS, cs, Akademie věd České republiky, abbr. AV ČR) was established in 1992 by the Czech National Council as the Czech successor of the former Czechoslovak Academy of Sciences and its tradition goes back ...

* The 2007

EATCS The European Association for Theoretical Computer Science (EATCS) is an international organization with a European focus, founded in 1972. Its aim is to facilitate the exchange of ideas and results among theoretical computer scientists as well as ...

Award for his contribution to theoretical computer science.

Carnegie Mellon University, 1981–2003

, 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 In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in math ...

, whereas the category of domains is not. In 1994, he was inducted as a

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

of the

Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ...

. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-07-14.

Bibliography

* With

, 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

, 1977. ''An Introduction to Modal Logic''. Oxford: Blackwell. *

References

External links

* *
DOMAIN 2002 Workshop on Domain Theory
' — held in honor of Scott's 70th birthday. * * * Dana Scott interviewed by

Gordon Plotkin Gordon David Plotkin, (born 9 September 1946) is a theoretical computer scientist in the School of Informatics at the University of Edinburgh. Plotkin is probably best known for his introduction of structural operational semantics (SOS) and h ...

, as part of the

series of interviews of Turing award winners
Part 1 (Nov 12, 2020)Part 2 (Dec 29, 2020)Part 3 (Jan 12, 2021)Part 4 (Feb 18, 2021)
{{DEFAULTSORT:Scott, Dana American computer scientists American logicians 1932 births Living people Members of the United States National Academy of Sciences Carnegie Mellon University faculty Fellows of the Association for Computing Machinery Fellows of the American Mathematical Society Fellows of Merton College, Oxford Formal methods people Lattice theorists Mathematical logicians Modal logicians Model theorists Programming language researchers Rolf Schock Prize laureates Semanticists Set theorists Topologists Turing Award laureates University of Chicago faculty University of California, Berkeley College of Letters and Science faculty Tarski lecturers Princeton University alumni UC Berkeley College of Letters and Science alumni People from Berkeley, California Engineers from California Scientists from California 20th-century American mathematicians 20th-century American engineers 21st-century American engineers 20th-century American scientists 21st-century American scientists 21st-century American mathematicians Gödel Lecturers