History of Relating Logic. The Origin and Research Directions

Mateusz Klonowski

doi:10.12775/LLP.2021.021

Authors

Mateusz Klonowski Departament of Logic, Nicolaus Copernicus University in Toruń https://orcid.org/0000-0001-8616-9189

DOI:

https://doi.org/10.12775/LLP.2021.021

Keywords

Epstein's Programme, relating logic, Torunian Programme of Relating Semantics

Abstract

In this paper, we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programme explores the various non-logical relationships in logical research, including those which are content-related. We will present a general description of relating logic and semantics as well as the most prominent issues regarding the Torunian Programme, including some of its special cases and the results achieved to date.

References

Carnielli, W. A., 1987, “Methods of proofs of relatedness and dependence logic”, Reports on Mathematical Logic 21: 35–46.

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

Epstein, R. L., 2005, “Paraconsistent logics with simple semantics”, Logique et Analyse 48 (189–192): 71–86.

Epstein, R. L., and S. Krajewski, 2004, “Relatedness predicate logic”, Bulletin of Advanced Reasoning and Knowledge 2: 19–38.

Epstein, R. L., and D. Walton, 1979, “Preface”, Philosophical Studies 36: 113–114.

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

Fariñas del Cerro, L.., and V. Lugardon, 1991, “Sequents for dependence logics”, Logique et Analyse 133/134: 57–71.

Fariñas del Cerro, L., and V. Lugardon, 1997, “Quantification and dependence logics”, pages 179–190 in S. Akama (ed.), Logic, Language and Computation. Applied Logic Series. Vol. 5, Springer Science+Business Media: Dordrecht. DOI: https://doi.org/10.1007/978-94-011-5638-7_9

Ferguson, T. M., 2017, Meaning and Prescription in Formal Logic. Variations on the Propositional Logic of William T. Parry, Trends in Logic, Vol. 54, Springer. DOI: https://doi.org/10.1007/978-3-319-70821-8

Iseminger, G., 1986, “Relatedness logic and entailment”, The Journal of Non-Classical Logic 3(1): 5–23.

Jarmużek, T., 2021, “Relating semantics as fine-grained semantics for intensional propositional logics”, pages 13–30 in A. Giordani, 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, 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 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 15: 517–536. DOI: https://doi.org/10.1007/s11787-021-00291-4

Krajewski, S., 1982, “On relatedness logic of Richard L. Epstein”, Bulletin of the Section of Logic 11 (1/2): 24–30.

Krajewski, S., 1986, “Relatedness Logic”, Reports on Mathematical Logic 20: 7–14.

Krajewski, S., 1991, “One or many logics? (Epstein’s set-assignement semantics for logical calculi)”, The Journal of Non-Classical Logic 8 (1): 7–33.

Ledda, A., F. Paoli and M. Pra 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, 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

Walton, D. N., 1985, “Pragmatic inferences about actions”, Synthese 65: 211–233. DOI: https://doi.org/10.1007/BF00869300

Wansing, H., 2020, “Connexive logic”, in E. N. Zalta (ed.), Stanford Encyclopedia of Philosophy, November 11, 2021. https://plato.stanford.edu/entries/logic-connexive/