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Logic and Logical Philosophy

Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems
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Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems

Authors

  • Tomasz Jarmużek Department of Logic Nicolaus Copernicus University in Toruń https://orcid.org/0000-0003-3456-3859
  • Francesco Paoli Department of Pedagogy, Psychology, Philosophy, University of Cagliari https://orcid.org/0000-0001-7915-3832

DOI:

https://doi.org/10.12775/LLP.2021.025

Keywords

: relating logic, relating semantics, logic of variable inclusion, history of relating logic, epistemic logic, deontic logic, incorporating relation

Abstract

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue.

References

Epstein, R. L., 1979, “Relatedness and implication”, Philosophical Studies 36: 137–173. DOI: https://doi.org/10.1007/BF00354267

Epstein, R. L., 1987, “The algebra of dependence logic”, Reports on Mathematical Logic 21: 19–34.

Epstein, R. L. (with the assistance and collaboration of: W. Carnielli, I. D’Ottaviano, S. Krajewski, R. Maddux), 1990, The Semantic Foundations of Logic. Volume 1: Propositional Logics, Springer Science+Business Media: Dordrecht. DOI: https://doi.org/10.1007/978-94-009-0525-2

Jarmużek, T., 2021, “Relating semantics as fine-grained semantics for intensional propositional logics”, pages 13–30 in A. Giordani and J. Malinowski (eds.), Logic in High Definition. Trends in Logical Semantics, Springer. DOI: https://doi.org/10.1007/978-3-030-53487-5_2

Jarmużek, T., and B. Kaczkowski, 2014, “On some logic with a relation imposed on formulae: tableau system F”, Bulletin of the Section of Logic 43(1/2): 53–72.

Jarmużek, T., and M. Klonowski, 2020, “On logics of strictly-deontic modalities. A semantic and tableau approach”, Logic and Logical Philosophy 29(3): 335–380. DOI: https://doi.org/10.12775/LLP.2020.010

Jarmużek, T., and M. Klonowski, 2021, “Some intensional logics defined by relating semantics and tableau systems”, pages 31–48 in A. Giordani and J. Malinowski (eds.), Logic in High Definition. Trends in Logical Semantics, Springer. DOI: https://doi.org/10.1007/978-3-030-53487-5_3

Jarmużek, T., and M. Klonowski, submitted, “Classical mono-relating logic. Theory and axiomatization”. Jarmużek, T., and M. Klonowski, manuscript, “Axiomatizing Boolean logics with relating implication defined by positive relational properties”.

Jarmużek, T., and J. Malinowski, 2019a, “Boolean connexive logics: semantics and tableau approach”, Logic and Logical Philosophy 28(3): 427–448. DOI: https://doi.org/10.12775/LLP.2019.003

Jarmużek, T., and J. Malinowski, 2019b, “Modal Boolean connexive logics: semantics and tableau approach”, Bulletin of the Section of Logic 48 (3): 213–243. DOI: https://doi.org/10.18778/0138-0680.48.3.05

Klonowski, M., 2018, “A Post-style proof of completeness theorem for Symmetric Relatedness Logic S”, Bulletin of the Section of Logic 47 (3): 201–214. DOI: https://doi.org/10.18778/0138-0680.47.3.05

Klonowski, M., 2019, “Aksjomatyzacja monorelacyjnych logik wiążących” (“Axiomatization of monorelational relating logics”), PhD thesis, Nicolaus Copernicus University in Toruń.

Klonowski, M., 2021, “Axiomatization of some basic and modal Boolean connexive logics”, Logica Universalis. DOI: https://doi.org/10.1007/s11787-021-00291-4

Ledda, A., F. Paoli, and M. P. Baldi, 2019, “Algebraic analysis of demodalised analytic implication”, Journal of Philosophical Logic 48: 957–979. DOI: https://doi.org/10.1007/s10992-019-09502-2

Malinowski, J., and R. Palczewski, 2021, “Relating semantics for connexive logic”, pages 49–65 in A. Giordani and J. Malinowski (eds.), Logic in High Definition. Trends in Logical Semantics, Springer. DOI: https://doi.org/10.1007/978-3-030-53487-5_4

Paoli, F., 1993, “Semantics for first degree relatedness logic”, Reports on Mathematical Logic 27: 81–94.

Paoli, F., 1996, “S is constructively complete”, Reports on Mathematical Logic 30: 31–47.

Paoli, F., 2007, “Tautological entailments and their rivals”, pages 153–175 in J. Y. Béziau, W. A. Carnielli and D. M. Gabbay (eds.), Handbook of Paraconsistency, College Publications: London.

Walton, D. N., 1979a, “Philosophical basis of relatedness logic”, Philosophical Studies 36 (2): 115–136. DOI: https://doi.org/10.1007/BF00354266

Walton, D. N., 1979b, “Relatedness in intensional action chains”, Philosophical Studies 36 (2): 175–223. DOI: https://doi.org/10.1007/BF00354268

Walton, D. N., 1982, Topical Relevance in Argumentation, John Benjamins Publishing Company: Amsterdam–Philadelphia. DOI: https://doi.org/10.1075/pb.iii.8

Logic and Logical Philosophy

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Published

2021-12-31

How to Cite

1.
JARMUŻEK, Tomasz and PAOLI, Francesco. Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems . Logic and Logical Philosophy. Online. 31 December 2021. Vol. 30, no. 4, pp. 563-577. [Accessed 2 July 2025]. DOI 10.12775/LLP.2021.025.
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Vol. 30 No. 4 (2021): December

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Copyright (c) 2021 Tomasz Jarmużek, Francesco Paoli

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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