Henrik Forssell

• Briseid, Eyvind Martol; Forssell, Henrik & Smestad, Bjørn (2025). Triangle and parallelogram area formulas: a critique of teacher education textbooks in Norway. NOMAD – Nordisk matematikkdidaktikk. ISSN 1104-2176. 30(2). doi: 10.7146/nomad.v30i2.162158. Full text in Research Archive Show summary

  We survey Norwegian textbooks for preservice teachers, looking for attention to generality in their presentations of diagrammatic proofs for the area formulas for triangles and parallelograms. We find that most textbooks do little to bring issues concerning generality to the attention of the reader in the presented arguments, neither explicitly nor implicitly. We also find that the textbooks fail, as a rule, to present correct proofs of the area formulas for parallelograms and triangles, even given a liberal view of what constitutes a proof. The presented proofs are incorrect in that they are insufficiently general; they fail to cover crucial cases. This is unfortunate, as preservice teachers should be made aware of issues concerning generality in diagrammatic proofs.

• Mathisen, Steinar; Sundtjønn, Trude & Forssell, Jon Henrik (2023). BlueBots and irrational numbers: Contingency moments in teaching mathematics and computational thinking in teacher education. In Drijvers, Paul; Csapodi, Csaba; Palmer, Hanna; Gosztonyi, Katalin & Kónya, Eszter (Ed.), Proceedings of the thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). European Society for Research in Mathematics Education. ISSN 9789637031045. p. 2736–2743. Full text in Research Archive
• Forssell, Henrik; Kharlamov, Evgeny & Thorstensen, Evgenij (2020). On equivalence and cores for incomplete databases in open and closed worlds. Leibniz International Proceedings in Informatics. 155, p. 1–21. doi: 10.4230/LIPIcs.ICDT.2020.10. Full text in Research Archive Show summary

  Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important questions are: whether one incomplete instance semantically implies another; when two are semantically equivalent; and whether a smaller or smallest semantically equivalent instance exists. For OWA and CWA these questions are fully answered. For several variants of OCWA, however, they remain open. In this work we adress these questions for Closed Powerset semantics and the OCWA semantics of [24]. We define a new OCWA semantics, called OCWA*, in terms of homomorphic covers that subsumes both semantics, and characterize semantic implication and equivalence in terms of such covers. This characterization yields a guess-and-check algorithm to decide equivalence, and shows that the problem is NP-complete. For the minimization problem we show that for several common notions of minimality there is in general no unique minimal equivalent instance for Closed Powerset semantics, and consequently not for the more expressive OCWA* either. However, for Closed Powerset semantics we show that one can find, for any incomplete database, a unique finite set of its subinstances which are subinstances (up to renaming of nulls) of all instances semantically equivalent to the original incomplete one. We study properties of this set, and extend the analysis to OCWA*

• Forssell, Jon Henrik; Gylterud, Håkon Robbestad & Spivak, David I (2020). Type theoretical databases. Journal of Logic and Computation. ISSN 0955-792X. 30(1), p. 217–238. doi: 10.1093/logcom/exaa009. Full text in Research Archive Show summary

  We show how the display-map category of finite (symmetric) simplicial complexes can be seen as representing the totality of database schemas and instances in a single mathematical structure. We give a sound interpretation of a certain dependent type theory in this model and show how it allows for the syntactic specification of schemas and instances and the manipulation of the same with the usual type-theoretic operations.

• Forssell, Henrik & Lumsdaine, Peter Lefanu (2019). Constructive Reflectivity Principles for Regular Theories. Journal of Symbolic Logic (JSL). ISSN 0022-4812. 84(4), p. 1348–1367. doi: 10.1017/jsl.2019.70. Full text in Research Archive
• Skjæveland, Martin G; Lupp, Daniel P.; Karlsen, Leif Harald & Forssell, Jon Henrik (2018). Practical Ontology Pattern Instantiation, Discovery, and Maintenance with Reasonable Ontology Templates. Lecture Notes in Computer Science (LNCS). ISSN 0302-9743. 11136, p. 477–494. doi: 10.1007/978-3-030-00671-6_28. Full text in Research Archive Show summary

  Reasonable Ontology Templates ( Open image in new window ) is a language for representing ontology modelling patterns in the form of parameterised ontologies. Ontology templates are simple and powerful abstractions useful for constructing, interacting with, and maintaining ontologies. With ontology templates, modelling patterns can be uniquely identified and encapsulated, broken down into convenient and manageable pieces, instantiated, and used as queries. Formal relations defined over templates support sophisticated maintenance tasks for sets of templates, such as revealing redundancies and suggesting new templates for representing implicit patterns. Ontology templates are designed for practical use; an Open image in new window vocabulary, convenient serialisation formats for the semantic web and for terse specification of template definitions and bulk instances are available, including an open source implementation for using templates. Our approach is successfully tested on a real-world large-scale ontology in the engineering domain.

• Forssell, Jon Henrik; Kharlamov, Evgeny & Thorstensen, Evgenij (2017). Towards characterising data exchange solutions in open and closedwords (extended abstract). CEUR Workshop Proceedings. 1912, p. 1–2. Full text in Research Archive
• Skjæveland, Martin G; Forssell, Jon Henrik; Kluwer, Johan Wilhelm; Lupp, Daniel Paul; Thorstensen, Evgenij & Waaler, Arild (2017). Pattern-Based Ontology Design and Instantiation with Reasonable Ontology Templates. CEUR Workshop Proceedings. 2043. Full text in Research Archive
• Skjæveland, Martin G; Forssell, Jon Henrik; Klüwer, Johan W.; Lupp, Daniel Paul; Thorstensen, Evgenij & Waaler, Arild (2017). Reasonable ontology templates: APIs for OWL: Efficient and practical ontology design and maintenance. CEUR Workshop Proceedings. 1963, p. 1–4. Full text in Research Archive
• Forssell, Jon Henrik; Lupp, Daniel Paul; Skjæveland, Martin G & Thorstensen, Evgenij (2017). Reasonable macros for ontology construction and maintenance. CEUR Workshop Proceedings. 1879, p. 1–13. Full text in Research Archive
• Forssell, Jon Henrik; Gylterud, Håkon Robbestad & Spivak, David I (2016). Type theoretical databases. Lecture Notes in Computer Science (LNCS). ISSN 0302-9743. 9537, p. 117–129. doi: 10.1007/978-3-319-27683-0_9. Full text in Research Archive
• Forssell, Henrik & Awodey, Steve (2013). First-order Logical Duality. Annals of Pure and Applied Logic. ISSN 0168-0072. doi: 10.1016/j.apal.2012.10.016. Full text in Research Archive
• Forssell, Henrik (2013). Subgroupoids and quotient theories. Theory and Applications of Categories. Full text in Research Archive
• Forssell, Jon Henrik (2012). Topological representation of geometric theories. Mathematical logic quarterly. ISSN 0942-5616. 58(6), p. 380–393. doi: 10.1002/malq.201100080. Full text in Research Archive
• Forssell, Henrik & Awodey, Steve (2005). Algebraic models of intuitionistic theories of sets and classes. Theory and Applications of Categories. Full text in Research Archive

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• Sundtjønn, Trude Pedersen; Mathisen, Steinar; Andreasen, Kristina Johnsdatter & Forssell, Jon Henrik (2024). How to prepare pre-service teachers to teach computational thinking in mathematics: Reflections after two iterations. Full text in Research Archive
• Forssell, Jon Henrik & Briseid, Eyvind Martol (2020). Feilaktige bevis for sanne påstander. Full text in Research Archive
• Forssell, Jon Henrik; Kharlamov, Evgeny & Thorstensen, Evgenij (2017). Towards Characterising Data Exchange Solutions in Open and Closed Words. CEUR Workshop Proceedings. 1912. Full text in Research Archive

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