Maximality of the Minimal R-Logic

Anna Maria Karczewska



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.


maximality; positional logics; connective of realization

Full Text:



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

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism