The World Wide Web Consortium (w3c) set Web Ontology Language (owl) and Shape Constraint Language (shacl) as international standards for managing semantically enriched data on the web. However, there is a difference in how these languages handle the completeness of data. In owl, not all information has to be explicitly present; part of the information can be implied by logical rules. Whereas shacl, which enables us to check for certain structures in a given knowledge graph, assumes completeness of it. Thus, with shacl we can validate the given data, while with owl we can infer knowledge. Combining the functionalities of the two into one standard is relevant and not straightforward.

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Public defence of Dominik Wehr’s Licentiate thesis.

Opponent Associate Professor Anupam Das, University of Birmingham
Examiner Docent Fredrik Engström, Göteborgs universitet

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It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. For modal logics, limit behavior for models and frames may differ. In 1994, Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5. They also proposed zero-one laws for the corresponding classes of frames, but their zero-one law for K-frames has since been disproved, and so has more recently their zero-one law for S4-frames.

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In 1994, Rineke Verbrugge did a postdoc in Gothenburg, as a scientific guest of Professor Per Lindström, who was writing his landmark book Aspects of Incompleteness at the time. Even though the two of them did not co-author any papers that year, there was still significant mutual influence and there were very lively discussions in the weekly seminars of the logic group. In this research lecture, Rineke Verbrugge will present some of the questions and results around bounded arithmetic, provability and interpretability logic that she was working on that year, for example, a small reflection principle for bounded arithmetic and the lattice of feasible interpretability types.