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

TLDR
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.

References

SHOWING 1-10 OF 21 REFERENCES

On Axioms and Rexpansions

We study the general problem of strengthening the logic of a given (partial) (non-deterministic) matrix with a set of axioms, using the idea of rexpansion. We obtain two characterization methods: a

Infectious semantics and analytic calculi for even more inclusion logics

TLDR
It is shown that non-determinism can be used to give simple and effective many-valued semantics to a range of companions of a given many- valued logic that result from filtering its inferences by requiring that variables of the premises and conclusion of an inference respect an inclusion requirement.

Analytic Calculi for Monadic PNmatrices

TLDR
It is proved that simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion, which seems to raise a contrast with recent non-analyticity results for sequent-calculi with PNmatrix semantics.

Possible-translations semantics for some weak classically-based paraconsistent logics

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

TLDR
The method is applicable to a large, central class of finite-valued logics with the language satisfying a certain minimal expressiveness condition and preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation.

Multi-valued Semantics: Why and How

TLDR
It is shown that one can get both modularity and analycity by using the semantic framework of multi-valued non-deterministic matrices, and that for using this framework in a constructive way it is best to view “truth-values” as information carriers, or “information- values”.

Tarskian consequence relations bilaterally: some familiar notions

TLDR
This paper is dedicated to developing a formalism that takes rejection seriously and shows how David Nelson’s logic N4 can be characterized bilaterally and the corresponding completeness result is proved.

5-VALUED NON-DETERMINISTIC SEMANTICS FOR THE BASIC PARACONSISTENT LOGIC mCi

TLDR
This paper presents a 5-valued characteristic nondeterministic matrix for mCi, which provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.

Axiomatizing non-deterministic many-valued generalized consequence relations

TLDR
It is shown that, under reasonable expressiveness requirements, simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion.