INSTANTIAL NEIGHBOURHOOD LOGIC

@article{Benthem2016INSTANTIALNL,
  title={INSTANTIAL NEIGHBOURHOOD LOGIC},
  author={Johan van Benthem and Nick Bezhanishvili and Sebastian Enqvist and Junhua Yu},
  journal={The Review of Symbolic Logic},
  year={2016},
  volume={10},
  pages={116 - 144}
}
Abstract This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness… 

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