Scott's past work in logic has concerned mainly model theory, automata, set theory, modal and intuitionistic logic, constructive mathematics, and connections between category theory and logic. His philosophical interests concern the foundations of logic, the philosophy of mathematics, and the semantical analysis of natural language. Work in computer science has been directed to developing the denotational semantics of programming languages and the mathematical foundations of a suitable theory of computability. Current research efforts aim at unifying the semantical approach with constructive logical formalisms to be able to give rigorous and machine-implementable proof methods and development tools for the inferential construction of correct programs. Part of the technique is based on the modelling of computational structures as partially ordered sets in special categories enjoying extensive closure conditions.

Background information and some of the mathematical aspects of this theory have been laid out in the jointly authored paper with Carl Gunter mentioned below. A recent development ties up topological spaces and computability; see the second paper cited. Other current projects involve work in symbolic mathematical computation and its uses in teaching. See the third article for an overview and indication of directions of future work. The hope is this work will also lead to better connections with information retrieval, electronic publishing, and more generally studies on the structure and production of electronic text.