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Ecumenical Propositional Tableau

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Abstract

Ecumenical logic aims to peacefully join classical and intuitionistic logic systems, allowing for reasoning about both classical and intuitionistic statements. This paper presents a semantic tableau for propositional ecumenical logic and proves its soundness and completeness concerning Ecumenical Kripke models. We introduce the Ecumenical Propositional Tableau (\(E_T\)) and demonstrate its effectiveness in handling mixed statements.

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References

  1. Marin, S., L.C. Pereira, E. Pimentel, and E. Sales, A Pure View of Ecumenical Modalities, in A Silva, R. Wassermann, R. de Queiroz, (eds.), Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings, Springer, 2021, pp. 388–407.

  2. Pereira, L.C., and E. Pimentel, On an ecumenical natural deduction with stoup–part i: the propositional case, arXiv preprint arXiv:2204.02199, 2022.

  3. Pereira, L.C., and R.O. Rodriguez, Normalization, soundness and completeness for the propositional fragment of prawitz cecumenical system, Revista Portuguesa de Filosofia 73(3):1153–1168, 2017.

    Article  Google Scholar 

  4. Pimentel, E., L.C. Pereira, and V. de Paiva, An ecumenical notion of entailment, Synthese 198(22):5391–5413, 2021.

    Article  MathSciNet  Google Scholar 

  5. Prawitz, D., Classical versus intuitionistic logic. in E.H. Haeusler, W. de Campos Sanz, and B. Lopes, (eds.), Why is this a Proof, College Publications, 2015, pp. 15–32.

  6. Priest, G., An Introduction to Non-Classical Logic: From If to Is, 2nd edn, Cambridge University Press, 2008; https://doi.org/10.1017/CBO9780511801174.

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Acknowledgements

The first author thanks the support of the São Paulo Research Foundation (FAPESP) through grant #21/01025-3, without which the present paper would not be possible. The second author acknowledges support from the National Council for Scientific and Technological Development (CNPq, Brazil), through the individual research grant #306530/2019-8. The authors also thank the organizers of the XX Brazilian Logic Conference (Salvador, Bahia, 2022) and everyone who contributed to this work with suggestions and insights. In special, we would like to thank the reviewer for his work and for all of the valuable suggestions that led to an improved version of our manuscript.

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Author notes

  1. Marcelo Coniglio, Bruno Lopes and Giorgio Venturi have contributed equally to this work.

Authors and Affiliations

  1. Instituto de Filosofia e Ciências Humanas, State University of Campinas, Campinas, SP, Brazil

    Renato Leme & Marcelo Coniglio

  2. Instituto de Computação, Fluminense Federal University, Niterái, RJ, Brazil

    Bruno Lopes

  3. Dipartimento di Civiltá e Forme del Sapere, University of Pisa, Pisa, Italy

    Giorgio Venturi

Authors
  1. Renato Leme
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  2. Marcelo Coniglio
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  3. Bruno Lopes
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  4. Giorgio Venturi
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Correspondence to Renato Leme.

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Special Issue: Contemporary Logic in Brazil Edited by Edward H. Haeusler, Ciro Russo, and Gisele Secco.

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Leme, R., Coniglio, M., Lopes, B. et al. Ecumenical Propositional Tableau. Stud Logica (2024). https://doi.org/10.1007/s11225-023-10091-0

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  • DOI: https://doi.org/10.1007/s11225-023-10091-0

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