ISSN: 1731-0555 eISSN: 2353-2998 OAI
DOI: 10.18276/cto.2023.39-08
Issue archive /
39/2023
Aksjomatyzacja czterowartościowej logiki modalnej Łukasiewicza
(Axiomatisation of Łukasiewicz's Four-Valued Logic)
| Authors: |
Mateusz
Lisowski
Katolicki Uniwersytet Lubelski Jana Pawła II |
| Keywords: | modal logic Łukasiewicz axiomatic systems |
| Whole issue publication date: | 2023 |
| Page range: | 19 (173-191) |
Abstract
The main subject of this article is the axiomatisation of Jan Łukasiewicz’s Ł-modal logic, a strict, regular, four-value modal logic whose matrix is a Cartesian product of two different two-value propositional matrices. Ł-modal logic was developed on the basis of philosophical discussions and logic research conducted in the Lviv-Warsaw school of logic, which focused on future contingents and temporal modalities. This article should deliver an overview of Ł-modal logic axiomatic systems and highlight differences and similarities between different axiomatic systems. To achieve this, it will describe properties of axiomatic systems, such as independence, simplicity, and the number of symbols used. These properties will then be used to analyse and compare selected axiomatisations. The analysis will be developed across (a) the original Łukasiewcz axiomatic system, which includes the prothotetic δ connective, (b) Lemmon’s axiomatic system, (c) Kripke’s axiomatic system, (d) Dywan’s axiomatic system, (e) Tkaczyk’s axiomatic system, with the jumping necessity theorem, (f) and axiomatic systems with a ternary connective.
Download file
Article file
Bibliography
| 1. | Dywan Z., Najkrótsze aksjomaty modalnej logiki Łukasiewicza, „Roczniki Filozoficzne” 64 (2016) 2, s. 5–9. |
| 2. | Font J.M., Hájek P., On Łukasiewicz’s Four-Valued Modal Logic, „Studia Logica: An International Journal for Symbolic Logic” 70 (2002) 2, s. 157–182. |
| 3. | Lemmon E.J., Algebraic Semantics for Modal Logics, „The Journal of Symbolic Logic” 31 (1966) 2, s. 191–218. |
| 4. | Łukasiewicz J., O zmiennych funktorach od argumentów zdaniowych, w: J. Słupecki (red.), Z zagadnień logiki i filozofii – pisma wybrane, PWN, Warszawa 1961. |
| 5. | Łukasiewicz J., System logiki modalnej, w: J. Słupecki (red.), Z zagadnień logiki i filozofii – pisma wybrane, PWN, Warszawa 1961. |
| 6. | Łukasiewicz J. , Uwagi filozoficzne o wielowartościowych systemach rachunku zdań, w: J. Słupecki (red.), Z zagadnień logiki i filozofii – pisma wybrane, PWN, Warszawa 1961. |
| 7. | Tkaczyk M., Futura Contingentia, Wydawnictwo KUL, Lublin 2015. |
| 8. | Tkaczyk M., On Axiomatization of Łukasiewicz’s Four-Valued Modal Logic, „Logic and Logical Philosophy” 20 (2011) 3, s. 215–232. |