Algorithmic correspondence and canonicity for non-distributive logics

@article{Conradie2019AlgorithmicCA,
  title={Algorithmic correspondence and canonicity for non-distributive logics},
  author={Willem Conradie and Alessandra Palmigiano},
  journal={Ann. Pure Appl. Log.},
  year={2019},
  volume={170},
  pages={923-974}
}

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References

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This work defines a suitable enhancement of the algorithm ALBA, which is used to prove the canonicity of certain syntactically defined classes of DLE-inequalities (called the meta-inductive inequalities), relative to the structures in which the formulas asserting the additivity of some given terms are valid.

Constructive Canonicity for Lattice-Based Fixed Point Logics

This result simultaneously generalizes Conradie and Craig's canonicity for $\mu$-inequalities based on a bi-intuitionistic bi-modal language, and ConradIE and Palmigiano's constructive canonicityFor inductive inequalities (restricted to normal lattice expansions to keep the page limit).

Constructive Canonicity of Inductive Inequalities

It is proved the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions, based on an application of the tools of unified correspondence theory.

Unified Correspondence as a Proof-Theoretic Tool

The present paper aims at establishing formal connections between correspondence phenomena, well known from the area of modal logic, and the theory of display calculi, originated by Belnap, and applies unified correspondence theory, with its tools and insights, to extend Kracht's results and prove his claims in the setting of DLE-logics.

Algorithmic correspondence and canonicity for possibility semantics

The present paper proves the soundness of the algorithm with respect to both full possibility frames and filter-descriptive possibility frames, and uses the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic).

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