Infinitary Domain Logic for Finitary Transition Systems

@inproceedings{Bonsangue1997InfinitaryDL,
  title={Infinitary Domain Logic for Finitary Transition Systems},
  author={Marcello M. Bonsangue and Joost N. Kok},
  booktitle={TACS},
  year={1997}
}
The Lindenbaum algebra generated by the Abramsky finitary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation. We extend Abramsky's result by proving that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain. As a consequence soundness and completeness of the infinitary logic is obtained for the class of finitary transition systems. A corollary of this result is that the… 
Toward an Infinitary Logic of Domains: Abramsky Logic for Transition Systems
TLDR
It is proved that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain.

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