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Duality for Finite Models: Relating Structure and Power

Project description

Uncovering the logic of computer science

Finite model theory (FMT) is a subarea of model theory – the branch of mathematical logic that deals with the link between a formal language and its interpretations. In contrast to model theory, FMT is explored using different tools and methods. Because of this, FMT has advanced separately from model theory, and the research communities and techniques are practically fragmented. The EU-funded D-FINED project will implement Stone duality – a distinct application of a topological method in algebra – to narrow the gap between the model theory’s semantics techniques and FMT’s combinatorial and complexity-theoretic ones. It should ultimately reinforce the links between mathematics and computer science.

Objective

"The present project is positioned in the research area of logic and semantics of computation, combining a rich mathematical theory with concrete applications in computer science. Finite model theory (FMT) is the specialisation of model theory to the class of finite models, and has been called ``the logic of computer science'' because in the latter field the basic models of computation are finite. Most of the classical results of model theory fail when restricted to finite models, hence FMT is studied using different tools and methods. For this reason, FMT has developed mostly independently from model theory and the research communities, as well as the techniques, are almost disjoint. FMT exemplifies a strand in the field of logic in computer science focussing on expressiveness and complexity (``Power""), as opposed to the one focussing on semantics and compositionality (``Structure""). In this project we will apply Stone duality to bridge the gap between the semantics methods of model theory, and the combinatorial and complexity-theoretic methods of FMT, i.e. to relate Structure and Power.

In his Ph.D. thesis, the applicant has successfully applied Stone duality and topology to the study of formal languages and logic on finite words. The proposed project constitutes both a natural continuation of this research line, generalising from finite words to finite models, and a novel approach to FMT. The applicant will collaborate with the supervisor, who is a leading expert in the interactions between logic and computational models arising in computer science.

An essential feature of this project is its high degree of interdisciplinarity, aiming to strengthen the connections between mathematics and computer science. The host institution, which is home to several experts in logic and foundations of computer science, will benefit from the applicant's experience in duality theory and topology, thus fostering cross-fertilisation within the European research community."

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Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Net EU contribution
€ 212 933,76
Address
Wellington square university offices
OX1 2JD Oxford
United Kingdom

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Region
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
Links
Other funding
€ 0,00