Descripción del proyecto
Descubrir la lógica de la informática
La teoría de modelos finitos (TMF) es una subárea de la teoría de modelos, la rama de la lógica matemática que se ocupa del vínculo entre un lenguaje formal y sus interpretaciones. A diferencia de la teoría de modelos, la TMF se explora utilizando herramientas y métodos alternativos. Por esta razón, la TMF ha avanzado al margen de la teoría de modelos, y las comunidades investigadoras y las técnicas de investigación están prácticamente fragmentadas. El proyecto D-FINED, financiado con fondos europeos, pondrá en práctica la dualidad de Stone —una aplicación específica de un método topológico en álgebra— para reducir la brecha entre las técnicas semánticas de la teoría de modelos y las técnicas combinatorias y de la teoría de la complejidad de la TMF. En última instancia, debería reforzar los vínculos entre las matemáticas y la informática.
Objetivo
"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."
Ámbito científico
Programa(s)
Régimen de financiación
MSCA-IF-EF-ST - Standard EFCoordinador
OX1 2JD Oxford
Reino Unido