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  1. Lauri Hella, Leonid Libkin & Juha Nurmonen (1999). Notions of Locality and Their Logical Characterizations Over Finite Models. Journal of Symbolic Logic 64 (4):1751-1773.
    Many known tools for proving expressibility bounds for first-order logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of (...)
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    Marcelo Arenas, Pablo Barceló & Leonid Libkin (2008). Game-Based Notions of Locality Over Finite Models. Annals of Pure and Applied Logic 152 (1):3-30.
    Locality notions in logic say that the truth value of a formula can be determined locally, by looking at the isomorphism type of a small neighbourhood of its free variables. Such notions have proved to be useful in many applications. They all, however, refer to isomorphisms of neighbourhoods, which most local logics cannot test. A stronger notion of locality says that the truth value of a formula is determined by what the logic itself can say about that small neighbourhood. Since (...)
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