Raymond Turner

I have one main area of research

No doubt the latter pair will become more central as I get older.

Logic and Computation

I take the central task of Theoretical Computing Science to be the construction of mathematical models of computational phenomena. Such models provide us with a deeper understanding of the nature of computation and representation. For example, the early work on computability theory provided a mathematical model of computation itself. Turing's work is of fundamental importance here. Adapting Gödel’s diagonalisation argument, he demonstrated that there are problems that do not admit of an algorithmic solution. He thus provided a mathematical model of computation that displayed its limitations. Later work on the semantics of programming languages enabled a precise articulation of the underlying differences between programming languages and led to a clearer understanding of the distinction between semantic representation and implementation. Early work in complexity theory supplied us with abstract notions which formally articulated informal ideas about the resources used during computation. I take this model building endeavour to be the central and fundamental role of theoretical computer science. It involves the construction of models from the Meccano-Kit supplied by 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. The following selected papers and books are some of my favourites[i]

The Logical Foundations of Specification

· The Foundations of Specification: Journal Logic and Computation

· Computability in Specification: Journal Logic and Computation

Computable Models

· Computable Models: Journal Logic and Computation

· Computable Models (Springer)

Types and Type Inference

· Type Inference for Set theory: Journal of Theoretical Computer Science

· Sets, Types and Type Checking: Journal Logic and Computation

· Types Handbook of Logic and Language

· Semantics and Stratification Journal Logic and Computation

· Logics of Truth. Notre Journal Formal Logic

· Truth and Modality for Knowledge Representation (MIT Press)

Formal Semantics

· Semantics and Property Theory Linguistics and Philosophy

· Properties, Relations and Propositions

· Properties, Types and Meaning Vol 1,2. Springer

The Philosophy of Computer Science

The Philosophy of Computer Science (PCS) is concerned with philosophical issues that arise from reflection upon the nature and practice of the academic discipline of Computer Science (CS). But what is the latter? It is certainly not just programming. After all, many people who write programs are not computer scientists. For example, physicists, accountants and chemists write programs. Indeed, computer science would be better described as being concerned with the meta-activity that is associated with programming. More generally, and more precisely, it is occupied with the design, development and investigation of the concepts and methodologies that facilitate and aid the specification, development, implementation and analysis of computational systems. Examples of this activity might include the design and analysis of programming, specification and architectural description languages; the construction and optimisation of compilers, interpreters, theorem provers and type inference systems; the invention of logical frameworks and the design of embedded systems, and much more. While one can argue about the exact phrasing of this characterisation of the discipline, its spirit seems to capture a core aspect of it. Certainly, many of the central philosophical questions of CS surround and underpin this activity, and many of them centre upon the logical, ontological and epistemological issues that concern it. However, in the end, computer science is what computer scientist do, and no exact formulaic definition can act as more than a guide to the discussion that follows. Indeed, the hope is that PCS will eventually contribute to a deeper understanding of the nature of the computer science.

· Understanding Programming Languages Minds and Machines

· The Philosophy of Computer Science Stanford Encyclopedia of Philosophy

· The Meaning of Programming Languages APA

I take the philosophy of computer science to underpin and guide more formal work in the logical and mathematical foundations of computer science. Such work is aimed at understanding computational systems rather than in their direct application.

The Philosophy of Mathematics

I have three current interests.

· Theories of Abstraction in Mathematics and Computer Science

· Wittgenstein’s Philosophy of Mathematics