Minimal non-relevant logics without the K axiom

• Autorzy: Robles G. , Mendez J. M.
• Języki publikacji: EN

Abstrakty

EN

The logic B+ is Routley and Meyer's basic positive logic. The logic BK+ is B+plus the K rule. We add to BK+ four intuitionistic-type negations. We show how to extend the resulting logics within the modal and relevance spectra. We prove that all the logics dened lack the K axiom.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2007
• Tom: No. 42
• Strony: 117--144
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Robles G.

autor

Mendez J. M.

• Department of Philosophy and Logic Universidad de Salamanca Campus Unamuno, Edicio FES E-37007 Salamanca, Spain,

Bibliografia

• [1] A.R. Anderson and N.D. Jr. Belnap, Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press, Princeton 1975.
• [2] A.R. Anderson, N.D. Jr. Belnap and J.M. Dunn, Entailment. The Logic of Relevance and Necessity, vol. II, Princeton University Press, Princeton 1992.
• [3] I. Hacking, What is strict implication, Journal of Symbolic Logic 28 (1963), pp. 51-71.
• [4] E.D. Mares, CE is not a conservative extension of E, Journal of Philosophical Logic 29 (2000), pp. 263-275.
• [5] J.M. Méndez and G. Robles, Relevance logics, paradoxes of consistency and the K rule. A quasi De Morgan negation (submitted).
• [6] J.M. Méndez, F. Salto, G. Robles, Anderson and Belnap's minimal positive logic with minimal negation, Reports on Mathematical Logic 36 (2002), pp. 117-130.
• [7] R.K. Meyer and R. Routley, Classical Relevant Logics I, Studia Logica 32 (1973), pp. 51-66.
• [8] R.K. Meyer and R. Routley, Classical Relevant Logics II, Studia Logica 33 (1974), pp. 183-194.
• [9] G. Robles, J.M. Méndez, F. Salto, Minimal negation in the ternary relational semantics, Reports on Mathematical Logic 39 (2005), pp. 47-65.
• [10] G. Robles, J.M. Méndez, F. Salto, Relevance logics, paradoxes of consistency and the K rule (contributed paper presented at the Logic Colloquium 2006, Nijmegen, The Netherlands July 27-August 2) Bulletin of Symbolic Logic (abstract accepted).
• [11] R. Routley et alii, Relevant Logics and their Rivals, vol. 1, Ridgeview Press, Ridgeview 1982.