Axiomatization of BLRI Determined by Limited Positive Relational Properties
Keywordsalgorithm α, Boolean logics with relating implication, BLRI, relating logic, relating semantics
In the paper a generalised method for obtaining an adequate axiomatic system for any relating logic expressed in the language with Boolean connectives and relating implication (BLRI), determined by the limited positive relational properties is studied. The method of defining axiomatic systems for logics of a given type is called an algorithm since the analysis allows for any logic determined by the limited positive relational properties to define the adequate axiomatic system automatically, step-by-step. We prove in the paper that the algorithm really works and we show how it can be applied to BLRI.
Epstein, R. L., 1979, “Relatedness and implication”, Philosophical Studies 36 (2): 137–173. DOI: https://doi.org/10.1007/BF00354267
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
Estrada-González, L., A. Giordani, T. Jarmużek, M. Klonowski, I. Sedlár and A. Tedder, 2021, “Incorporating the relation into the language? A survey of approaches in relating logic”, Logic and Logical Philosophy 30 (4): 711–739. DOI: https://doi.org/10.12775/LLP.2021.014
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, 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-a, “Classical mono-relating logics. Theory and axiomatization”.
Jarmużek, T., and M. Klonowski, submitted-b, “The algorithm α as a general method of axiomatization of relating logics”.
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 F. Paoli, 2021, “Relating logic and relating semantics. History, philosophical applications and some of technical problems”, Logic and Logical Philosophy 30 (4): 563–577. DOI: https://doi.org/10.12775/LLP.2021.025
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., 2021a, “Axiomatization of some basic and modal Boolean connexive logics”, Logica Universalis 15 (4): 517–536. DOI: https://doi.org/10.1007/s11787-021-00291-4
Klonowski, M., 2021b, “History of relating logic. The origin and research directions” Logic and Logical Philosophy 30 (4): 579–629. DOI: https://doi.org/10.12775/LLP.2021.021
Malinowski, J., and R. Palczewski, 2021, “Relating semantics for connexive logic”, pages 49–65 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_4
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.
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