Logic@GU

We provide an algebraic definition of “fragment of geometric logic”. Those are understood as families of locales enjoying algebraic properties. Meet-semilattices, Distributive lattices, and other relevant classes of posets corresponding to established propositional logics arise as fragments of geometric logic in this sense. Thanks for the modularity of our approach we can tell what family of fragments of geometric logic verify a completeness theorem (with respect to booleans), Craig-interpolation, and Beth definability. In its current form, the framework cannot encompass modal logics, as modal operators are structure (as opposed to property). This is a report of joint work with Lingyuan Ye.

Sun Tzu was a military strategist who lived in China about 2500 years ago. His book is still popular today, especially in business circles.

This talk presents a study of “The Art of War” from the perspectives of logic, mathematics, and computer science. We explain briefly what a mind map is and our strict text tree interpretation of it, for the purpose of analyzing Sun Tzu’s text. We show that you can improve the translation and find more meaning in the text, representing the text as mind maps. If time permits, we will illustrate that, surprisingly, the text still helps us to understand what is happening in warfare today.

The title of this talk is also the title of our book, co-authored by Kaibo Xie (Tsinghua Univ. Beijing), and Bonan Zhao (Univ. of Edinburgh), and published in 2022 by Springer. The book is the result of a joint study of the Institute of Language, Logic and Computation, Univ. of Amsterdam and the Institute for Philosophy, Tsinghua University, Beijing, China.

Frame definability is a well-studied notion for a plethora of logics: a class of frames is defined by a set of formulas if and only if such formulas are validities for all and only the frames in such class.

In this talk, I will present a series of results about frame definability in a fragment of conditional logic. Conditional logic is an extension of propositional logic that includes a binary “counterfactual” conditional operator \(\leadsto\). We specifically make the following choices: (i), we consider the non-nested fragment of conditional logic (i.e., where conditionals are not allowed in the scope of other conditionals), and (ii), we consider only finite posets as the underlying structure of the models of our logic. Given these assumptions, a formula of the form \(\varphi \leadsto \psi\) is intuitively true if the consequent \(\psi\) is true in all the minimal (with respect to the partial order of the poset) worlds where the antecedent \(\varphi\) is true. Via these semantics, this fragment of conditional logic becomes relevant in several fields, such as default reasoning and belief revision.

I will present the following results: (i) a set of non-nested conditional formulas each defining a different class of finite posets; (ii) a characterization theorem identifying the classes of finite posets that can be defined by a non-nested conditional formula; and (iii), a Sahlqvist-like theorem proving that every class of finite posets definable via a non-nested conditional formula is definable also by a first-order formula.

This talk is based on the paper Frame Definability in Conditional Logic, a joint work with Damiano Fornasiere and Johannes Marti, which was published at AiML 2024.

Opponent: Jakub Szymanik, Associate professor at the Center for Brain/Mind Sciences and the Computer Science Department at the University of Trento.

Abstract Description logics are designed to reason efficiently with ontologies in knowledge bases, which are widely used in several industries. Human errors commonly cause mistakes to occur in the axioms of these ontologies, which leads to the logics deducing false conclusions. Ontology engineers spend much time on finding these false axioms to repair the ontology. This process can be facilitated by presenting a justification of the false conclusion, i.e. a set of axioms that entail the conclusion. Typically, the number of justifications for a given conclusion is very large and it is not clear which one should be presented.

It is therefore useful to estimate the cognitively adequate complexity of description logic so that the simplest justification(s) can be identified and selected. This work focusses on the cognitive complexity of deciding the consistency of ABoxes in the description logic $\mathcal{ALE}$. Conceptual considerations entail that the complexity of the ABox consistency problem is expressed as a linear preorder on a large enough set of ABoxes. This linear preorder can be estimated by an ACT-R model called SHARP. The model is a tableau algorithm implemented in a cognitive architecture, thereby modelling a human brain executing the tableau algorithm, which forms an approximation of the cognitive complexity ordering.

A complexity ordering that is a linear preorder can be obtained from experimental data by aggregating the different individual orders from a sample into one so-called proto-order, in which the largest transitive subrelation is the desired linear pre-order. The predicted complexity ordering by SHARP agrees well with the empirical data.

To enable applications in ontology debugging, a surrogate model is needed that accurately approximates SHARP’s output with great computational efficiency. Such a surrogate model can be obtained by the Random Forest algorithm trained on an appropriate dataset generated by SHARP. The complexity ordering thus obtained agrees well with the one predicted by SHARP but can be estimated in a fraction of the time enabling it for practical applications.

A workshop dedicated to current and future trens in cyclic and illfounded notions of provability and justification. The event is sponsored by the Knut and Alice Wallenberg Foundation via the research project Taming Jörmungandr: The Logical Foundations of Circularity and the Department of Philosophy, Linguistics and Theory of Science.

Confirmed Speakers

• Henning Basold (Leiden University)
• Anupam Das (University of Birmingham)
• Sebastian Enqvist (Stockholm University)
• Iris van der Giessen (University of Amsterdam)
• Marianna Girlando (University of Amsterdam)
• Helle Hvid Hansen (University of Groningen), TBC
• Alex Leitsch (TU Wien)
• Reuben Rowe (Royal Holloway)
• Alexis Saurin (IRIF)
• Takeshi Tsukada (Chiba University)

Location

The workshop will be held at the Faculty of Humanities of the University of Gothenburg, address Renströmsgatan 6, Gothenburg. It is adjacent to the Korsvägen transport hub and within walking distance from the city centre.

Schedule

Morning of Wednesday, 24 September until afternoon of Friday, 26 September 2025.