# Datalog-Expressibility for Monadic and Guarded Second-Order Logic

@inproceedings{Bodirsky2021DatalogExpressibilityFM, title={Datalog-Expressibility for Monadic and Guarded Second-Order Logic}, author={Manuel Bodirsky and Simon Kn{\"a}uer and Sebastian Rudolph}, booktitle={ICALP}, year={2021} }

We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all integers l,k, there exists a *canonical* Datalog program Pi of width (l,k), that is, a Datalog program of width (l,k) which is sound for C (i.e., Pi only derives the goal predicate on a finite…

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On Logics and Homomorphism Closure

- Mathematics2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2021

This work investigates several problems regarding the homomorphism closure (homclosure) of the class of all (finite or arbitrary) models of logical sentences: membership of structures in a sentence’s homclosure; sentence homclosedness; homclosure characterizability in a logic; normal forms for homclosed sentences in certain logics.

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