Proof Search on Bilateralist Judgments over Non-deterministic Semantics

Greati, Vitor Rodrigues; Marcelino, Sérgio; Marcos, João

doi:10.1007/978-3-030-86059-2_8

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…Another direction for future research worth mentioning is the study of these and other logics associated to the algebra B u (and other three-valued algebras) in the setting of different kinds of H-systems. In particular, a twodimensional version of Set-Set H-systems [21,23], whose induced logics are the so-called B-consequence relations [5], may be employed as a uniform setting for investigating pure consequence relations (like BK and PWK), their intersection (order-theoretic consequence relations) and mixed consequence relations (we use here the terminology of [16]), the latter being non-Tarskian consequence relations (lacking either reflexivity [26] or transitivity [19]).…”

Section: Discussionmentioning

confidence: 99%

Finite Hilbert Systems for Weak Kleene Logics

Greati,

Marcelino,

Rivieccio

2024

Stud Logica

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Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.

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Section: Discussionmentioning

confidence: 99%

Finite Hilbert Systems for Weak Kleene Logics

Greati,

Marcelino,

Rivieccio

2024

Stud Logica

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Finite Two-Dimensional Proof Systems for Non-finitely Axiomatizable Logics

Greati

Marcos

2022

Automated Reasoning

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The characterizing properties of a proof-theoretical presentation of a given logic may hang on the choice of proof formalism, on the shape of the logical rules and of the sequents manipulated by a given proof system, on the underlying notion of consequence, and even on the expressiveness of its linguistic resources and on the logical framework into which it is embedded. Standard (one-dimensional) logics determined by (non-deterministic) logical matrices are known to be axiomatizable by analytic and possibly finite proof systems as soon as they turn out to satisfy a certain constraint of sufficient expressiveness. In this paper we introduce a recipe for cooking up a two-dimensional logical matrix (or -matrix) by the combination of two (possibly partial) non-deterministic logical matrices. We will show that such a combination may result in -matrices satisfying the property of sufficient expressiveness, even when the input matrices are not sufficiently expressive in isolation, and we will use this result to show that one-dimensional logics that are not finitely axiomatizable may inhabit finitely axiomatizable two-dimensional logics, becoming, thus, finitely axiomatizable by the addition of an extra dimension. We will illustrate the said construction using a well-known logic of formal inconsistency called mCi. We will first prove that this logic is not finitely axiomatizable by a one-dimensional (generalized) Hilbert-style system. Then, taking advantage of a known 5-valued non-deterministic logical matrix for this logic, we will combine it with another one, conveniently chosen so as to give rise to a -matrix that is axiomatized by a two-dimensional Hilbert-style system that is both finite and analytic.

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Proof Search on Bilateralist Judgments over Non-deterministic Semantics

Cited by 2 publications

References 22 publications

Finite Hilbert Systems for Weak Kleene Logics

Finite Hilbert Systems for Weak Kleene Logics

Finite Two-Dimensional Proof Systems for Non-finitely Axiomatizable Logics

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