Proof Search on Bilateralist Judgments over Non-deterministic Semantics

@inproceedings{Greati2021ProofSO,
  title={Proof Search on Bilateralist Judgments over Non-deterministic Semantics},
  author={Vitor Rodrigues Greati and S{\'e}rgio Marcelino and J. Martin Marcos},
  booktitle={TABLEAUX},
  year={2021}
}
The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional notion of entailment induced by semantic structures that also accommodate non-deterministic and partial interpretations, and propose a prooftheoretical apparatus to reason over bilateralist judgments using symmetrical two-dimensional analytical Hilbert-style… 

Finite two-dimensional proof systems for non-finitely axiomatizable logics

A recipe for cooking up a two-dimensional logical matrix by the combination of two (possibly partial) non-deterministic logical matrices is introduced and it is shown that such a combination may result in B -matrices satisfying the property of sufficient expressiveness.

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