Maximality of the Minimal R-Logic

• Authors: Karczewska Anna Maria
• Languages of publication: EN

Abstracts

The minimal system of the connective of realization – T. Jarmużek and A. Pietruszczak’s MR– is examined. The single-index rule is defined. Then it is claimed that if a single– index rule non-derivable in MR is derivable in a strengthening of MR, then the strengthening is inconsistent. This property may be called the single-index maximality.

Keywords

EN

maximality; positional logics; connective of realization

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2018
• Volume: 27
• Issue: 2
• Pages: 193-203

Dates

published

2018-06-15

Contributors

author

Karczewska Anna Maria

• Anna Maria Karczewska The John Paul II Catholic University of Lublin Faculty of Philosophy Lublin, Poland

References

• Garson, J.W., Modal Logic for Philosophers, Cambridge University Press, 2006.
• Jarmużek, T., and A. Pietruszczak, “Completeness of Minimal Positional Calculus”, Logic and Logical Philosophy 13 (2004): 147–162. DOI: 10.12775/LLP.2004.009
• Jarmużek, T., and M. Tkaczyk, Normalne logiki pozycyjne (Normal Positional Logics), Wydawnictwo KUL, Lublin, 2015.
• Łoś J., “Podstawy analizy metodologicznej kanonów Milla” (The foundations of methodological analysis of Mill’s canons), Annales Universitatis Mariae Curie-Skłodowska 2 (1947): 269–301.
• Pogorzelski, W.A., and P. Wojtylak, Completeness Theory for Propositional Logics, Birkhäuser, Berlin, 2008.
• Rescher, N., and A. Urquhart, Temporal Logic, Springer-Verlag, New York and Vienna, 1971.
• Tkaczyk, M., Logika czasu empirycznego (Logic of empirical time), Wydawnictwo KUL, Lublin, 2009.
• Tkaczyk, M., “Negation in Weak Positional Calculi”, Logic and Logical Philosophy 22 (2013): 3–19. DOI: 10.12775/LLP.2013.001