Dana Scott

Dana Stewart Scott (born October 11, 1932) is an American logician who 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.

He received his B.A. 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.

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.

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.

He proved that the axiom of constructibility is incompatible with the existence of a measurable cardinal, a result considered seminal in the evolution of set 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 Lopez-Escobar (Infinitely Long Formulas with Countable Quantifier Degrees).

After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960.

Scott also began working on modal logic in this period, beginning a collaboration with John Lemmon, who moved to Claremont, California, in 1963.

John Lemmon and Scott began work on a modal-logic textbook that was interrupted by Lemmon's death in 1966.

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.

Later, Scott and Montague independently discovered an important generalisation of Kripke semantics for modal and tense logic, called Scott-Montague semantics (Scott 1970).

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 the University of Oxford in 1972.

He was member of Merton College while at Oxford and is now an Honorary Fellow of the college.

This period saw Scott working with Christopher Strachey, 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.

One of Scott's contributions is his formulation of domain 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 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 is not.

His work on automata theory earned him the 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 also worked on modal logic, topology, and category theory.

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 Boolean-valued model, as Solovay and Petr Vopěnka did likewise at around the same time.

In 1994, he was inducted as a Fellow of the Association for Computing Machinery.

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 was especially interested in Arthur Prior's approach to tense logic 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.

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 with Tarski and became part of the group that surrounded him, including me and Richard 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. 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.""

In 2012 he became a fellow of the American Mathematical Society.