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

List of Fellows of the American Mathematical Society

retrieved 2013-07-14.

''Modal logic''

Arthur Prior

In the

''Alfred Tarski: life and logic''

Cambridge University Press, , . * Solomon Feferman (2005)

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''.

DOMAIN 2002 Workshop on Domain Theory

' — held in honor of Scott's 70th birthday. * * * Dana Scott interviewed by Gordon Plotkin, as part of the

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

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 practical disciplines (includin ...

, 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. S ...

, and Mathematical Logic
Mathematical logic is the study of 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 formal s ...

at 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 Technolog ...

; 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 Em ...

. 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 comp ...

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. He has worked also on modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

, topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

, 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, cat ...

.
Early career

He received his B.A. in Mathematics from theUniversity 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 sc ...

while at Princeton, and defended his thesis in 1958. Solomon Feferman (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 ...

, 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
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 ...

. This work led to the joint bestowal of 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 comp ...

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 theUniversity 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 ...

, and involved himself with classical issues in mathematical logic
Mathematical logic is the study of 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 formal s ...

, 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 concer ...

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 ...

.
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 onmodal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

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 (L ...

, who moved to Claremont, California
Claremont () is a suburban city on the eastern edge of Los Angeles County, California, United States, east of downtown Los Angeles. It is in the Pomona Valley, at the foothills of the San Gabriel Mountains. As of the 2010 census it had a popu ...

, in 1963. Scott was especially interested in Arthur Prior'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 (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 ...

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, Scott formulated the concept of Boolean-valued model, as Solovay andPetr 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 ...

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 awa ...

. 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 theUniversity 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, ...

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

This period saw Scott working withChristopher 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., ...

, 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
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 circumscribe th ...

. 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 compute ...

, 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, store, and distribute information. From a sociotechnical perspective, information systems are composed by four components: task, people, ...

.
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 profess ...

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

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

AtCarnegie 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 Technolog ...

, 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 m ...

, 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 educatio ...

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 membe ...

. 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 ...

.retrieved 2013-07-14.

Bibliography

* 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. * WithJohn 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 (L ...

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

Further reading

*Blackburn, de Rijke and Venema (2001)''Modal logic''

Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer.
Cambridge University Pres ...

.
* Jack Copeland (2004)Arthur Prior

In the

Stanford Encyclopedia of Philosophy
The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. ...

.
* Anita Burdman Feferman and Solomon Feferman (2004).''Alfred Tarski: life and logic''

Cambridge University Press, , . * Solomon Feferman (2005)

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
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962.
History
The MIT Press traces its origins back to 1926 when MIT publis ...

.
External links

* *DOMAIN 2002 Workshop on Domain Theory

' — held in honor of Scott's 70th birthday. * * * Dana Scott interviewed by Gordon Plotkin, as part 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 membe ...

series of interviews of Turing award winnersPart 1 (Nov 12, 2020)

{{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