Welcome to the webpage of the logic group at the University of Gothenburg. Information about our research and activities can be found through the links to the left. More detailed information is available through the personal pages of group members and our homepage at the University of Gothenburg.

Past talks can be found on the seminar page. Links to forthcoming talks are distributed via the seminar mailing list.

Nordic Online Logic Seminar

Øystein Linnebo
(University of Oslo) – Potentialism in the philosophy and foundations of mathematics
Aristotle famously claimed that the only coherent form of infinity is potential, not actual. However many objects there are, it is possible for there to be yet more; but it is impossible for there in fact to be infinitely many objects. Although this view was superseded by Cantor’s transfinite set theory, even Cantor regarded the collection of all sets as “unfinished” or incapable of “being together”. In recent years, there has been a revival of interest in potentialist approaches to the philosophy and foundations of mathematics. The lecture provides a survey of such approaches, covering both technical results and associated philosophical views, as these emerge both in published work and in work in progress.

This talk is part of the Nordic Online Logic Seminar.

Mauricio Martel
(CSE, GU) – On the Complexity of Conservative Extensions in the Two-Variable Guarded Fragment

Conservative extensions are a fundamental notion in logic. In the area of description logic, deciding whether a logical theory is a conservative extension of another theory is a fundamental reasoning problem with applications in ontology engineering tasks, such as ontology modularity, ontology reuse and ontology versioning. It has been observed in recent years that conservative extensions are decidable in many modal and description logics, given that they can often be characterized elegantly in terms of appropriate notions of bisimulations. But no work has been done for more expressive logics such as the two-variable fragment and the guarded fragment, which are considered to be generalizations of modal and description logics, and are typically used to explain their good computational behavior.

Lindström Lecture

Sara Negri
(University of Genoa) – Syntax and semantics in synergy
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.

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.