Mathematical logic studies the properties of logics, understood as formal languages. In his monograph dissertation in mathematics, Reijo Jaakkola develops and investigates several such logics with important applications in theoretical computer science. The thesis first examines the guarded fragment, a well-studied logic with strong computational and model-theoretic properties. It shows that although the full fragment lacks the Craig interpolation property, two natural syntactic restrictions restore it while preserving many of the guarded fragment’s desirable features. The thesis also studies Boolean modal logics, which can be used for reasoning about relational structures. It proves that their computational complexity remains unchanged when the usual restriction to binary relations is lifted and relations of arbitrary arity are allowed. Finally, Jaakkola introduces static computation logic, establishes its fundamental properties, and connects it with a fragment of least fixed-point logic. This shows that the logic captures polynomial-time computation over ordered finite structures.
The doctoral dissertation of Master of Science Reijo Jaakkola, entitled Results on Computational Logics: Complexity, Expressivity and Model Theory, in the field of mathematics, will be publicly examined at the Faculty of Information Technology and Communication Sciences at Tampere University on Wednesday, 19 August 2026.
The opponent will be Professor Lidia Tendera from the University of Opole, Poland. The custos will be Associate Professor Antti Kuusisto from the Faculty of Information Technology and Communication Sciences.