I have worked in a range of areas of mathematical logic and theoretical
computer science, including type theory and logical frameworks, proof
theory, categorical logic, substructural logic, resource semantics, and
process algebra. In theses areas, I have always been particularly
interested in the interplay between syntax and semantics.
In recent years, I have become engaged with mathematical systems
modelling, with a particular interest in applying --- in the style of
classical mathematical modelling as practised in, for example,
engineering, where the control of complexity by abstraction is
critically important in delivering useful models --- the ideas of
compositional semantics and logic to complex systems, particularly in
the social sciences and systems engineering. Computer security, system
security, and information security provide excellent challenges for this
approach. All this began around 2004, with an extended stay with the
security research group at HP Labs, initially funded by a Royal Society
- The design and mathematical theory of substructural logics. For example, classical,
intuitionistic, and modal bunched logics: relational semantics, algebraic semantics,
duality theory, tableaux and other proof systems.
- Resource semantics.
- Logics for complex systems modelling. For example, classical and intuitionistic
layered graph logics and their applications in systems and security modelling.
- Logical models of information and information flow.
- The logical and mathematical theory of proof-search.
- Logical models of decision-making in security.
- Conceptual and mathematical models of distributed systems and of security architectures.
- The design and use as modelling languages of logics and process algebras based on resource semantics.
- Modelling of information an resource flows in complex systems.
- Utility- and logic-based representations of trust in systems models.
- Security policy and security management, particularly from an economics-based perspective
- Information stewardship and its economics, a notion that extends core security
concepts to address issues such as sustainability and resilience
- Logical models of access control policies and systems.