Squares in Fork Arrow Logic

@article{Freitas2003SquaresIF,
  title={Squares in Fork Arrow Logic},
  author={Renata P. de Freitas and Petrucio Viana and M. Benevides and Sheila R. M. Veloso and Paulo A. S. Veloso},
  journal={Journal of Philosophical Logic},
  year={2003},
  volume={32},
  pages={343-355}
}
In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is… 

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