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 characterised 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. 1932 (MCMXXXII) was a leap year starting on Friday (the link will take you to a full 1932 calendar). ... Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... The Philosopher (detail), by Rembrandt Philosophy is a study that includes diverse subfields such as aesthetics, epistemology, ethics, logic, and metaphysics. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Carnegie Mellon University Carnegie Mellon University is a private research university located in Pittsburgh, Pennsylvania. ... Berkeley as seen from the Claremont Canyon Regional Preserve. ... Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Euclid, detail from The School of Athens by Raphael. ... The Philosopher (detail), by Rembrandt Philosophy is a study that includes diverse subfields such as aesthetics, epistemology, ethics, logic, and metaphysics. ... The factual accuracy of this article is disputed. ... The A.M. Turing Award is given annually by the Association for Computing Machinery to a person selected for contributions of a technical nature made to the computing community. ... 1976 (MCMLXXVI) was a leap year starting on Thursday (the link is to a full 1976 calendar). ... Christopher Strachey (1916–1975) was a British computer scientist. ... The 1970s decade refers to the years from 1970 to 1979, inclusive. ... In theoretical computer science formal semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation. ... A modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... Logical Methods in Computer Science is a new journal in theoretical computer science and applied logic. ...

Early career

He received his BA in Mathematics from the University of California, Berkeley in 1954. BA or Ba may stand for: // Abbreviations Bachelor of Arts, see Bachelors degree barium (Ba), the chemical symbol for the chemical element Bashkir language (ISO 639 alpha-2, ba) Boston and Albany Railroad (AAR reporting mark BA) Corporations & institutions Boeing Company (stock symbol) British Airways British Association for the... It has been suggested that UC Mens Chorale be merged into this article or section. ... 1954 (MCMLIV) was a common year starting on Friday of the Gregorian calendar. ...

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. Doctor of Philosophy, or Ph. ... Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ... 1958 (MCMLVIII) was a common year starting on Wednesday of the Gregorian calendar. ... The University of Chicago is a private university principally located in the Hyde Park neighborhood of Chicago, Illinois, founded in 1890 and opened in 1892. ...

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. 1959 (MCMLIX) was a common year starting on Thursday of the Gregorian calendar. ... Michael Oser Rabin (born 1931 in Breslau, Germany, today in Poland) is a noted computer scientist and a recipient of the Turing Award, the most prestigious award in the field. ... The factual accuracy of this article is disputed. ... The A.M. Turing Award is given annually by the Association for Computing Machinery to a person selected for contributions of a technical nature made to the computing community. ... In computer science, computational complexity theory is the branch of the theory of computation that studies the resources, or cost, of the computation required to solve a given problem. ...

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. 1960 (MCMLX) was a leap year starting on Friday (the link is to a full 1960 calendar). ... Template:C20YearInnTopic 1963 (MCMLXIII) was a common year starting on Tuesday (the link is to a full 1963 calendar). ... It has been suggested that UC Mens Chorale be merged into this article or section. ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ...

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. James S. Halpern (born New York, 1945) is a judge of the United States Tax Court. ...

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). A modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... Edward John Lemmon (1 June 1930-29 July 1966) was a logician and philosopher born in Sheffield, UK. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously (Lemmon and Scott, 1977). ... Claremont is a city located in Los Angeles County, California, USA, about 45 kilometers (30 miles) east of downtown Los Angeles at the base of the San Gabriel Mountains. ... Template:C20YearInnTopic 1963 (MCMLXIII) was a common year starting on Tuesday (the link is to a full 1963 calendar). ... In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. ... Richard Merett Montague (1930–1971) was an American mathematician and philosopher. ... Kripke semantics (also known as possible world semantics, relational semantics, or frame semantics) is a formal semantics for modal logic systems, created in late 1950s and early 1960s by Saul Kripke. ...

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). 1966 (MCMLXVI) was a common year starting on Saturday (the link is to a full 1966 calendar). ... Kripke semantics (also known as possible world semantics, relational semantics, or frame semantics) is a formal semantics for modal logic systems, created in late 1950s and early 1960s by Saul Kripke. ...

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. Template:C20YearInnTopic 1963 (MCMLXIII) was a common year starting on Tuesday (the link is to a full 1963 calendar). ... 1972 (MCMLXXII) was a leap year starting on Saturday (the link is to a full 1972 calendar). ... Robert M. Solovay is a set theorist who spent many years as a professor at UC Berkeley. ... In mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure or model, in which the truth values of propositions are not limited to true and false, but take values in some fixed complete Boolean algebra. ... Petr VopÄ›nka (1935-) is one of the world’s leading mathematicians. ... 1967 (MCMLXVII) was a common year starting on Sunday of the Gregorian calendar (the link is to a full 1967 calendar). ... In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ... Paul Joseph Cohen (born April 2, 1934) is an American mathematician. ... 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. ... 1972 (MCMLXXII) was a leap year starting on Saturday (the link is to a full 1972 calendar). ...

Oxford University, 1972–1981

Dana Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of Oxford University in 1972. 1972 (MCMLXXII) was a leap year starting on Saturday (the link is to a full 1972 calendar). ... 1981 (MCMLXXXI) was a common year starting on Thursday of the Gregorian calendar. ... The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ... 1972 (MCMLXXII) was a leap year starting on Saturday (the link is to a full 1972 calendar). ...

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. Christopher Strachey (1916–1975) was a British computer scientist. ... In computer science, denotational semantics is an approach to formalizing the semantics of computer systems by constructing mathematical objects (called denotations or meanings) which express the semantics of these systems. ... Computer science (informally, CS or compsci) is, in its most general sense, the study of computation and information processing, both in hardware and in software. ... Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Domain theory is a branch of mathematics that studies special kinds of partially ordered sets commonly called domains. ... It has been suggested that Information system be merged into this article or section. ...

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.

This article is about the year. ... The Harold Pender Award, initiated in 1972, 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 profession who has achieved distinction by significant contributions to society. ... 1997 (MCMXCVII in Roman) is a common year starting on Wednesday of the Gregorian calendar. ... The Schock Prizes were instituted by the will of philosopher and artist Rolf Schock (1933-1986). ... The Royal Swedish Academy of Sciences or , founded in 1739 by King Frederick I, is one of the Royal Academies in Sweden. ... 2001: A Space Odyssey. ...

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 is not. 1981 (MCMLXXXI) was a common year starting on Thursday of the Gregorian calendar. ... 2003 (MMIII) was a common year starting on Wednesday of the Gregorian calendar. ... Carnegie Mellon University Carnegie Mellon University is a private research university located in Pittsburgh, Pennsylvania. ... 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. ...

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.

Michael Oser Rabin (born 1931 in Breslau, Germany, today in Poland) is a noted computer scientist and a recipient of the Turing Award, the most prestigious award in the field. ... Edward John Lemmon (1 June 1930-29 July 1966) was a logician and philosopher born in Sheffield, UK. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously (Lemmon and Scott, 1977). ...

Other works

• Blackburn, de Rijke and Venema, 2001. Modal logic. Cambridge University Press.
• Jack Copeland, 2004. Arthur Prior. In the Stanford Encyclopedia of Philosophy.

The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ...

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