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Dana Stewart Scott | |
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| Born | (1932-10-11)October 11, 1932 (age 93) |
| Education | University of California, Berkeley (BA) Princeton University (MA,PhD) |
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| Thesis | Convergent Sequences of Complete Theories (1958) |
| Doctoral advisor | Alonzo Church |
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Dana Stewart Scott (born October 11, 1932) is an American logician who is theHillman University Professor emeritus ofComputer Science,Philosophy, andMathematical Logic atCarnegie Mellon University.[1] He is now retired and lives inBerkeley, California. He andMichael O. Rabin won the 1976 ACMTuring Award for their work onautomata theory, while his collaborative work withChristopher Strachey in the 1970s laid the foundations of modern approaches to thesemantics of programming languages. He has also worked onmodal logic,topology, andcategory theory.
He received hisB.A. in Mathematics from theUniversity of California, Berkeley, in 1954. He wrote hisPh.D. thesis onConvergent Sequences of Complete Theories under the supervision ofAlonzo Church while 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 withTarski and 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.[2] 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 Award on the two, for the introduction of this fundamental concept ofcomputational complexity theory.
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 theory and Tarskianmodel theory. He proved that theaxiom of constructibility is incompatible with the existence of ameasurable cardinal, a result consideredseminal in the evolution of set theory.[3]
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 also began working onmodal logic in this period, beginning a collaboration withJohn Lemmon, who moved toClaremont, California, in 1963. Scott was especially interested inArthur Prior's approach totense logic and 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 semantics for 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 of thecanonical model that 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).
Following an initial observation ofRobert Solovay, Scott formulated the concept ofBoolean-valued model, as Solovay andPetr 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 thecontinuum hypothesis to that provided byPaul Cohen. This work led to the award of theLeroy P. Steele Prize in 1972.
Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of theUniversity of Oxford in 1972. He was member ofMerton College while at Oxford and is now an Honorary Fellow of the college.
This period saw Scott working withChristopher Strachey, and the twomanaged, 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:
AtCarnegie Mellon University, Scott proposed the theory ofequilogical spaces as a successor theory to domain theory; among its many advantages, the category of equilogical spaces is acartesian closed category, whereas the category of domains[4] is not. In 1994, he was inducted as aFellow of theAssociation for Computing Machinery. In 2012 he became a fellow of theAmerican Mathematical Society.[5]
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| Preceded by | President of theDLMPST/IUHPST 1983–1987 | Succeeded by |
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