How to bereally contraction free
- Greg Restall
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A logic is said to becontraction free if the rule fromA → (A →B) toA →B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there isanother contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to berobustly contraction free if there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free.
- N. D. Belnap,A Useful Four-Valued Logic, in J. M. Dunn and G. Epstein (eds.) Modern Uses of Multiple-Valued Logics, D. Reidel Publ. Co., Dordrecht.
- J. M. Dunn,Intuitive Semantics for First-Degree Entailments and ‘Coupled Trees’ Philosophical Studies 29 (1976), pp. 139–168.
- J. M. Dunn, andG. Epstein, (eds)Modern Uses of Multiple-Valued Logics D. Reidel Publ. Co., Dordrecht 1977.
- R. K. Meyer, S. Giambrone andR. T. Brady,Where Gamma Fails Studia Logica 43 (1984), pp. 247–256.
- R. K. Meyer andJ. K. Slaney,Abelian Logic (from A to Z) in G. Priest, R. Routley and J. Norman (eds)Paraconsistent Logic: Essays on the Inconsistent Philosophia Verlag, München, 1989.
- G. Priest, R. Routley andJ. Norman (eds),Paraconsistent Logic: Essays on the Inconsistent Philosophia Verlag, München, 1989.
- M. Shaw-Kwei,Logical Paradoxes for Many-Valued Systems Journal of Symbolic Logic 19 (1954), pp. 37–40.
- J. K. Slaney,The Implications of Paraconsistency Proceedings of IJCAI-91, Vol.2 (1991), pp. 1052–1057.
- J. K. Slaney, T. Surendonk andR. Girle,Time, Truth and Logic, Australian National University, Automated Reasoning Project Technical Report, TR-ARP-11/89, 1989.
- R. B. White,The Consistency of the Axiom of Comprehension in the Infinite-Valued Predicate Logic of Łukasiewicz Journal of Philosophical Logic 8 (1979), pp. 509–534.
- How to bereally contraction free
Volume 52, Issue 3 , pp 381-391
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- Kluwer Academic Publishers
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- Greg Restall (1)
- Author Affiliations
- 1. Philosophy Department, The University of Queensland, 4072, Queensland, Australia