Negation in weak positional calculi

Marcin Tkaczyk



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.


negation; distribution; positional; many-valued

Full Text:



Belnap, N. D., “How a computer should think”, pages 30-56 in Contemporary Aspects of Philosophy, G. Ryle (ed.), Stockfield 1976.

Jarmużek, T., and A. Pietruszczak, “Completeness of Minimal Positional Calculus”, Logic and Logical Philosophy 13 (2004): 147-162.

Kleene, S. C., Introduction to Metamathematics, North-Holland 1952.

Łoś, J., “Podstawy analizy metodologicznej kanonów Milla”, Annales Universitatis Mariae Curie-Skłodowska 2 (1948): 269-301.

Priest, G., “The logic of paradox”, Journal of Philosophical Logic 8 (1979): 219-241.

Raju, P. T., “The principle of four-cornered negation in Indian philosophy”, Review of Metaphysics 7 (1954): 694-713.

Rescher, N., and A. Urquhart, Temporal Logic, Vienna 1971.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism