# First-Order Logic with Counting: At Least, Weak Hanf Normal Forms Always Exist and Can Be Computed!

@article{Kuske2017FirstOrderLW, title={First-Order Logic with Counting: At Least, Weak Hanf Normal Forms Always Exist and Can Be Computed!}, author={Dietrich Kuske and Nicole Schweikardt}, journal={ArXiv}, year={2017}, volume={abs/1703.01122} }

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… CONTINUE READING

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