Axiomatization of BLRI Determined by Limited Positive Relational Properties

Tomasz Jarmużek; Mateusz Klonowski

doi:10.12775/LLP.2022.003

Authors

Tomasz Jarmużek Department of Logic Nicolaus Copernicus University in Toruń https://orcid.org/0000-0003-3456-3859
Mateusz Klonowski Department of Logic Nicolaus Copernicus University in Toruń https://orcid.org/0000-0001-8616-9189

DOI:

https://doi.org/10.12775/LLP.2022.003

Keywords

algorithm α, Boolean logics with relating implication, BLRI, relating logic, relating semantics

Abstract

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.

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