Analytic Tableaux for Non-deterministic Semantics

Grätz, Lukas

doi:10.1007/978-3-030-86059-2_3

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…Based on the ideas proposed in the present paper, in[Coniglio and Toledo, 2021] were introduced (n + 2)-valued tableau systems for da Costa's paraconsistent logics C n . General approaches to tableau proof systems for finite non-deterministic matrices can be found in[Pawlowski, 2020] and[Grätz, 2021a].…”

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Tableau systems for some Ivlev-like (quantified) modal logics

Coniglio¹,

Cerro²,

Peron³

2022

Preprint

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Ivlev's pioneering work started in the 1970's showed a new and promissory way in the study of modal logic from the perspective of many-valued logics. Continuing our previous work on Ivlev-like non-normal modal logics with non-deterministic semantics, we present in this paper tableau systems for Tm, S4m and S5m, the non-normal versions of T, S4 and S5, respectively, as well as for their corresponding first-order extensions Tm*, S4m* and S5m*.

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confidence: 99%

Tableau systems for some Ivlev-like (quantified) modal logics

Coniglio¹,

Cerro²,

Peron³

2022

Preprint

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A Uniform Formalisation of Three-Valued Logics in Bisequent Calculus

Indrzejczak,

Petrukhin

2023

Lecture Notes in Computer Science

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We present a uniform characterisation of three-valued logics by means of bisequent calculus (BSC). It is a generalised form of sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents. This family covers several forms of hypersequent and nested sequent calculi introduced to provide decent SC for several non-classical logics. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, this reasonably modest generalization of standard SC is sufficient. In this paper we examine a variety of three-valued logics and show how they can be formalised in the framework of bisequent calculus. All provided systems are cut-free and satisfy the subformula property. Also the interpolation theorem is constructively proved for some logics.

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Two Decision Procedures for da Costa’s $$C_n$$ Logics Based on Restricted Nmatrix Semantics

Coniglio

Toledo

2021

Stud Logica

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Analytic Tableaux for Non-deterministic Semantics

Cited by 4 publications

References 23 publications

Tableau systems for some Ivlev-like (quantified) modal logics

Tableau systems for some Ivlev-like (quantified) modal logics

A Uniform Formalisation of Three-Valued Logics in Bisequent Calculus

Two Decision Procedures for da Costa’s $$C_n$$ Logics Based on Restricted Nmatrix Semantics

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