The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue). If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.
The seminar is open to public and does not require any form of registration.
We introduce the logic FOCN(ℙ) which extends first-order logic by counting and by numerical predicates from a set ℙ, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature.
We obtain a locality result showing that every FOCN(ℙ)-formula can be transformed into a formula in Hanf normal form that is equivalent on all finite structures of degree at most d. A formula is in Hanf normal form if it is a Boolean combination of formulas describing the neighbourhood around its tuple of free variables and arithmetic sentences with predicates from ℙ over atomic statements describing the number of realisations of a type with a single centre. The transformation into Hanf normal form can be achieved in time elementary in d and the size of the input formula. From this locality result, we infer the following applications: