Logic at GU
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.
The model SHARP is a result of (somewhat naively) implementing a tableaux-based reasoning algorithm of the description logic ALE into the cognitive architecture ACT-R. Its aim is to predict the inference time of human performance on deciding inconsistency of an ALE ABox, thereby giving rise to a complexity measure on ABoxes that is cognitively adequate. Ten predictions following from SHARP are tested against empirical data and their implications for the model are discussed.
Around 1930 a major paradigm shift occurred in the foundations of mathematics; we may call it the METAMATHEMATICAL TURN. Until then the task of a logician had been to design and explain a full-scale formal language that was adequate for the practice of mathematical analysis in such a way that the axioms and rules of inference of the theory were rendered evident by the explanations.
The Logic Group at the University of Gothenburg hosts its annual World Logic Day Pub Quiz. For information of this and other World Logic Day events around the world, see http://wld.cipsh.international/wld2024.html.
There is a mature body of work in logic aiming to characterize logical formalisms in terms of their structural or model-theoretic properties. The origins of this work can be traced to Alfred Tarski’s program to characterize metamathematical notions in “purely mathematical terms” and to Per Lindström’s abstract characterizations of first-order logic. For the past forty years, rule-based logical languages have been widely used in databases and in related areas of computer science to express integrity constraints and to specify transformations in data management tasks, such as data exchange and ontology-based data access. The aim of this talk is to present an overview of more recent results that characterize various classes of rule-based logical languages in terms of their structural or model-theoretic properties.
A classical result by Lovász asserts that two graphs G and H are isomorphic if and only if they have the same left profile, that is, for every graph F, the number of homomorphisms from F to G coincides with the number of homomorphisms from F to H. A similar result is also known to hold for right profiles, that is, two graphs G and H are isomorphic if and only if for every graph F, the number of homomorphisms from G to F coincides with the number of homomorphisms from H to F. During the past several years, there has been a study of equivalence relations that are relaxations of isomorphism obtained by restricting the left profile or the right profile to suitably restricted classes of graphs, instead of the class of all graphs. Furthermore, a notion of a query algorithm based on homomorphism counts was recently introduced and investigated. The aim of this talk is to present an overview of some of the main results in this area with emphasis on the differences between left homomorphism counts and right homomorphism counts.