Syntax and semantics, often considered as conflicting aspects of logic, have turned out to be intertwined in a methodology for generating complete proof systems for wide families of nonclassical logics. In this formal semantics, models can be considered as purely mathematical objects with no ontological assumptions upon them. More specifically, by the “labelled formalism”, which now is a welldeveloped methodology, the semantics is turned into an essential component in the syntax of logical calculi. Thus enriched, the calculi not only constitute a tool for the automatisation of reasoning, but can also be used at the metalevel to establish general structural properties of logical systems and direct proofs of completeness up to decidability in the terminating case. The calculi, on the other hand, can be used to find simplified models through conservativity results. The method will be illustrated with gradually generalised semantics, including topological ones such as neighbourhood semantics.
The 2022 Lindström Lectures were delivered in June 2022 by Sara Negri, Professor of Mathematics at the University of Genoa.
The Public Lindström Lecture took place on Monday, 20 June 2022 at the Faculty of Humanities of Gothenburg University and online. Details are available on the GU page about the lectures.
The Research Lecture took place on Wednesday, 22 June 2022 at the Department of Philosohy, Linguistics and Theory of Science.

Public Lindström Lecture: Sara Negri (University of Genoa)
Syntax and semantics in synergy

Research Lindström Lecture: Sara Negri (University of Genoa)
On modal embeddings
Motivated by the difficulty in proving faithfulness of various modal embeddings (starting with Gödel’s translation of intuitionistic logic into S4), we use labelled calculi to obtain simple and uniform faithfulness proofs for the embedding of intermediate logics into their modal companions, and of intuitionistic logic into provability logic, including extensions to infinitary logics.