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Aksjomatyzacja czterowartościowej logiki modalnej Łukasiewicza
Lisowski, Mateusz (Wydawnictwo Naukowe Uniwersytetu Szczecińskiego, 2023)
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 philosophica 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.