A Pure View of Ecumenical Modalities

Marin, Sonia; Pereira, Luiz Carlos; Pimentel, Elaine; Sales, Emerson

doi:10.1007/978-3-030-88853-4_24

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…This section is devoted to present the pure label free calculus for ecumenical modalities introduced in [23], where every basic object of the calculus can be translated as a formula in the language of the logic.…”

Section: A Nested System For Ecumenical Modal Logicmentioning

confidence: 99%

“…the ecumenical birelational semantics. Please refer to [23] for a more detailed presentation. Definition 5.9.…”

Section: [γ]mentioning

confidence: 99%

“…In this work, we bring new basis for ecumenical systems, where systems and results presented in [22,23] fit smoothly. More specifically, this work improves the op.cit.…”

Section: Introductionmentioning

confidence: 96%

“…2. A new pure labeled system for modalities comes naturally in this approach, and the nested system in [23] is easily proven correct and complete w.r.t. it.…”

Section: Introductionmentioning

confidence: 99%

“…This involves a non-trivial use of polarities, as well as a non-standard proof of cut-elimination. We show that, is one is not careful, the quest for purity ends up in collapsing; Section 4 extends the propositional fragment of LCE with modalities, resulting in a new pure labeled ecumenical modal system (labEK); Section 5 brings the nested ecumenical system nEK from [23], which is naturally seen as the label-free counterpart of labEK; Section 6 briefly discusses fragments, axioms and extensions and Section 7 discusses related and future work, and concludes the paper.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Separability and harmony in ecumenical systems

Marı́n¹,

Pereira²,

Pimentel³

et al. 2022

Preprint

Self Cite

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The quest of smoothly combining logics so that connectives from classical and intuitionistic logics can co-exist in peace has been a fascinating topic of research for decades now. In 2015, Dag Prawitz proposed a natural deduction system for an ecumenical first-order logic. We start this work by proposing a pure sequent calculus version for it, in the sense that connectives are introduced without the use of other connectives. For doing this, we extend sequents with an extra context, the stoup, and define the ecumenical notion of polarities. Finally, we smoothly extend these ideas for handling modalities, presenting pure labeled and nested systems for ecumenical modal logics.

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Section: A Nested System For Ecumenical Modal Logicmentioning

confidence: 99%

“…the ecumenical birelational semantics. Please refer to [23] for a more detailed presentation. Definition 5.9.…”

Section: [γ]mentioning

confidence: 99%

“…In this work, we bring new basis for ecumenical systems, where systems and results presented in [22,23] fit smoothly. More specifically, this work improves the op.cit.…”

Section: Introductionmentioning

confidence: 96%

“…2. A new pure labeled system for modalities comes naturally in this approach, and the nested system in [23] is easily proven correct and complete w.r.t. it.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Separability and harmony in ecumenical systems

Marı́n¹,

Pereira²,

Pimentel³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Ecumenical Propositional Tableau

Leme,

Coniglio,

Lopes

et al. 2024

Stud Logica

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On Combining Intuitionistic and S4 Modal Logic

Rasga,

Sernadas

2024

B Sect Log

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We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality.We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. The calculus is proved to be sound and complete with respect to this semantics. We also show that the combined logic is a conservative extension of each component. Finally we establish that the Gentzen calculus for the combined logic enjoys cut elimination.

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A Pure View of Ecumenical Modalities

Cited by 3 publications

References 17 publications

Separability and harmony in ecumenical systems

Separability and harmony in ecumenical systems

Ecumenical Propositional Tableau

On Combining Intuitionistic and S4 Modal Logic

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