42nd  Top people by Erd%C5%91s number: #2 
45th  Top logicians 
Dana Stewart Scott  



Born 
October 11, 1932 
Fields  Computer Science Mathematics Philosophy 
Institutions  University of
California, Berkeley Oxford University Carnegie Mellon University 
Doctoral advisor  Alonzo Church 
Doctoral students  Angus
Macintyre Marko Petkovšek 
Notable awards  ACM Turing Award 1976, Tarski lectures 1989 
Dana Stewart Scott (born October 11, 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 characterized 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 editorinchief of the new journal Logical Methods in Computer Science.
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He received his BA in Mathematics from the University of California, Berkeley, in 1954. 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. Solomon Feferman (2005) writes of this period:
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, 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.
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.
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 LopezEscobar (Infinitely Long Formulas with Countable Quantifier Degrees). Scott's work as research supervisor has been an important source of his intellectual influence.
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 naturallanguage 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 were independently to discover an important generalisation of Kripke semantics for modal and tense logic, called ScottMontague semantics (Scott 1970).
John Lemmon and Scott began work on a modallogic 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).
Following an initial observation of Robert Solovay, Scott formulated the concept of Booleanvalued 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 Booleanvalued 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.
Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of Oxford University in 1972.
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 ScottStrachey approach to denotational semantics; 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 loopingcontrol 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.
Scott's work of this period led to the bestowal of:
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^{[2]} is not. In 1994 he was inducted as a Fellow of the Association for Computing Machinery.


