Minimal non-relevant logics without the K axiom II. Negation introduced via the unary connective

• Autorzy: Robles G.
• Języki publikacji: PL

Abstrakty

EN

In the first part of this paper (RML No. 42) a spectrum of constructive logics without the K axiom is defined. Nega- tion is introduced with a propositional falsity constant. The aim of this second part is to build up logics definitionally equivalent to those displayed in the first part, negation being now introduced as a primitive unary connective. Relational ternary semantics is provided for all logics defined in the paper.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2010
• Tom: Vol. 45
• Strony: 97--118
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Robles G.

• Dpto. de Historia y Filosofia de la CC, la Ed. y el Leng. Universidad de La Laguna Facultad de Filosofia, Campus de Guajara 38071, La Laguna, Tenerife, Spain,

Bibliografia

• [1] H. Andréka, J. X.Madar´asz and I. Nemeti, Mutual definability does not imply definitional equivalence, a simple example, Mathematical Logic Quaterly 51 (2005), pp.591–597.
• [2] A. Church, Introduction to Mathematical logic, Edition revised and enlarged, Princeton,Princeton University Press, 1996.
• [3] G. Robles, The basic constructive logic for negation-consistency, Journal of Logic Language and Information 17/2 (2008), pp. 161–181.
• [4] G. Robles and J. M. Méndez, On defining constructive negation in logics of entailment, in Dimensions of Logical Concepts, (ed. by Jean-Yves Béziau and Alexandre Costa-Leite) Colecao CLE, volumen 54, UNICAMP, Campinas, Brazil. ISBN: 978-85-86497-05-6, 2009, 265-277.
• [5] G. Robles and J. M. Méndez, Minimal non-relevant logics without the K axiom,Reports on Mathematical Logic 42 (2007), pp. 117–144.
• [6] R. Routley, R. K. Meyer, V. Plumwood and R. T. Brady, Relevant Logics and their Rivals, vol. 1, Atascadero, CA, Ridgeview Publishing Co., 1982.
• [7] J. Slaney, MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide, Canberra, Australian National University, 1995. URL: http://users.rsise.anu.edu.au/˜jks