Maximality of the Minimal R-Logic
DOI: http://dx.doi.org/10.12775/LLP.2017.008
Abstract
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.
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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
Print ISSN: 1425-3305
Online ISSN: 2300-9802