Negation in Weak Positional Calculi

• Authors: Marcin Tkaczyk
• Languages of publication: EN

Abstracts

EN

Four weak positional calculi are constructed and examined. They refer to the use of the connective of negation within the scope of the positional connective “R” of realization. The connective of negation may be fully classical, partially analogical or independent from the classical, truth- functional negation. It has been also proved that the strongest system, containing fully classical connective of negation, is deductively equivalent to the system MR from Jarmużek and Pietruszczak.

Keywords

EN

negation; distribution; positional; many-valued

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2013
• Volume: 22
• Issue: 1
• Pages: 3-19

Dates

published

2013-03-01

online

2013-07-02

Contributors

author

Marcin Tkaczyk

• Departament of Logic Catholic University of Lublin ul. Pszenna 9 20-617 Lublin, Poland

References

• [1] Belnap, N.D., “How a computer should think”, pages 30-56 in Contempo-rary Aspects of Philosophy, G. Ryle (ed.), Stockfield 1976.
• [2] Jarmużek, T., and A. Pietruszczak, “Completeness of Minimal Positional Calculus”, Logic and Logical Philosophy 13 (2004): 147-162.
• [3] Kleene, S.C., Introduction to Metamathematics, North-Holland 1952.
• [4] Łoś, J., “Podstawy analizy metodologicznej kanonow Milla”, Annales Uni-versitatis Mariae Curie-Skłodowska 2 (1948): 269-301.
• [5] Priest, G., “The logic of paradox”, Journal of Philosophical Logic 8 (1979): 219-241.
• [6] Raju, P.T., “The principle of four-cornered negation in Indian philosophy”, Review of Metaphysics 7 (1954): 694-713.
• [7] Rescher, N., and A. Urquhart, Temporal Logic, Vienna 1971.

Identifiers

DOI

10.12775/LLP.2013.001