Incorporating the Relation into the Language? A Survey of Approaches in Relating Logic

Luis Estrada-González; Alessandro Giordani; Tomasz Jarmużek; Mateusz Klonowski; Igor Sedlár; Andrew Tedder

doi:10.12775/LLP.2021.014

Authors

Luis Estrada-González Institute for Philosophical Research, National Autonomous University of Mexico (UNAM) https://orcid.org/0000-0002-1466-0240
Alessandro Giordani Faculty of Letters and Philosophy, Catholic University of Milan https://orcid.org/0000-0003-4654-2174
Tomasz Jarmużek https://orcid.org/0000-0003-3456-3859
Mateusz Klonowski Nicolaus Copernicus University in Toruń. Department of Logic https://orcid.org/0000-0001-8616-9189
Igor Sedlár https://orcid.org/0000-0002-1942-7982
Andrew Tedder https://orcid.org/0000-0002-7378-4673

DOI:

https://doi.org/10.12775/LLP.2021.014

Keywords

incorporating relation, object language, relating logic, relating semantics

Abstract

In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.

References

Anderson, A. R., and N. D. Belnap., 1975, Entailment: The Logic of Relevance and Necessity, Volume I, Princeton University Press.

Areces, C., P. Blackburn and M. Marx, 2001, “Hybrid logics: Characterization, interpolation and iomplexity”, Journal of Symbolic Logic 66 (3): 977–1010.

Artemov, S., and M. Fitting, 2019, Justification Logic: Reasoning with Reasons, New York: Cambridge University Press.

Avron, A., 2014, “What is relevance logic?”, Annals of Pure and Applied Logic 165: 26–48.

Blackwell, A. F., 2008, “Cognitive dimensions of notations: understanding the ergonomics of diagram use”, pages 5–8 in G. Stapleton; J. Howse and J. Lee (eds.), Diagrammatic Representation and Inference, Berlin: Springer.

Barceló, A., 2016, “Las imágenes como herramientas epistémicas”, scientiae studia, 14 (1): 45–63.

Baker, A., 2003, “Quantitative parsimony and explanatory power”, British Journal for the Philosophy of Science 54(2): 245–259.

Bellucci, F., A. Moktefi and A.-V. Pietarinen, 2018, “Simplex sigillum veri: Peano, Frege, and Peirce on the primitives of logic”, History and Philosophy of Logic 39(1): 80–95.

Booth, D., 1991, “Logical feedback”, Studia Logica 50 (2): 225–239.

Carnielli, W. A., M. E. Coniglio and J. Marcos, 2014, “Logics of formal inconsistency”, pages 1–93 in D. M. Gabbay, F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 14. Springer, Dordrecht.

Dutilh Novaes, C., 2012, Formal Languages in Logic. A Philosophical and Cognitive Analysis, Cambridge University Press.

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: Dordrecht. DOI: https://doi.org/10.1007/978-94-009-0525-2

Fagin, R., and J. Y. Halpern, 1988, “Belief, awareness and limited reasoning”, Artificial Intelligence 34: 39–76. DOI: https://doi.org/10.1016/0004-3702(87)90003-8

Gabbay, D. M., 2014, “Introduction to labelled deductive systems”, pages 179–266 in D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 17. Springer, Dordrecht.

Humberstone, L., 2011, The Connectives, MIT Press.

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 T. Kupś, 2020, “The heritage of Jerzy Łoś’s philosophical logic and the Polish question. An introduction to the volume”, in the special issue: “The heritage of Jerzy Łoś’s philosophical logic”, Studia z Historii Filozofii 3 (11): 93-107.

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

Jarmużek, T., and M. Tkaczyk, 2019, “Expressive power of the positional operator R: a Case Study in Modal Logic and Modal Philosophy”, Ruch Filozoficzny 2: 93–107.

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, “Axiomatization of monorelational relating logics” (in Polish: “Aksjomatyzacja monorelacyjnych logik wiążących”) 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

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., 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.

Russell, G., 2017, “An introduction to logical nihilism”, pages 125–155 in H. Leitgeb, I. Niiniluoto, P. Seppälä and E. Sober (eds.), Logic, Methodology and Philosophy of Science. Proceedings of the 15th International Congress, College Publications: London.

Scott, D. S., 1973, “Background to formalization”, pp. 244–273 in H. Leblanc (ed.), Truth, Syntax and Modality, North-Holland: Amsterdam, 1973.

Wansing, H., 1998, Displaying Modal Logic, Springer: Dordrecht. Woleński, J., 1989, Logic and Philosophy in the Lvov-Warsaw School, Kluwer: Dordrecht.