University of Essex

Faculty Member, School of Computer Science and Electronic Engineering

Emeritus Professor of Logic and Computation

About

My main research interests are

1. LOGIC AND COMPUTATION

I take the central task of Theoretical Computing Science to be the construction of mathematical models of computational phenomena. This involves the construction of models using logic, algebra, topology and set theory and, indeed, any branch of mathematics that proves useful. Such models provide the means of exploring the properties and limitations of computational concepts and systems that would otherwise be unavailable.  In particular, mathematical and philosophical logic have supplied a rich source of such models. Conversely, computer science has inspired the development of new areas of logic. Linear logic and dynamic logic are two well known examples. It is in this interplay between logic and computation where much of my research resides.

2. THE PHILOSOPHY OF COMPUTER SCIENCE

The Philosophy of Computer Science is concerned with philosophical issues that arise from reflection upon the nature and practice of the academic discipline of computer science. In this sense, it parallels the philosophies of mathematics and physics in being a parasitic philosophical discipline. But while physics and mathematics are well established disciplines, with broad agreement concerning their subject matter, computer science is new, its very nature unfixed and unclear. So part of the task will be to provide a somewhat clearer view of the content and personality of the subject.

3. TYPED PREDICATE LOGIC

Typed predicate logic was developed to offer a unifying framework for many of the current logical systems, and especially those that employ some notion of type or sort. These include the simple and ramified type theories of Principia Mathematica, the intensional simple type theory of Montague, intensional ramified type theories, logics of properties and truth, constructive type theories, theories of operations and types and the Calculi of Constructions. A basic introduction may be found in my teaching material.

4. FOUNDATIONS OF MATHEMATICS

I am concerned with Local Formalisation – the formalisation of informal theories that are subareas or branches of mathematics. While no piece of mathematics can be totally isolated, one can uncover the fundamental concepts of an area or approach. For example, Bishop’s constructive mathematics relies on notions of natural number, class and operation, geometry relies on some notions of line, point and set and category theory on arrows and objects.

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