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 non-classical 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 well-developed 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 meta-level 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 Department of Philosophy, Linguistics and Theory of Science at the University of Gothenburg launched a lecture series in 2013 to celebrate the singular achievements of Per Lindström, former professor of logic at the department.