David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 52 (3):381 - 391 (1993)
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 (with the standard connectives) are shown to be robustly contraction free.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
J. Michael Dunn (1976). Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'. Philosophical Studies 29 (3):149-168.
Robert K. Meyer, Steve Giambrone & Ross T. Brady (1984). Where Gamma Fails. Studia Logica 43 (3):247 - 256.
Moh Shaw-Kwei (1954). Logical Paradoxes for Many-Valued Systems. Journal of Symbolic Logic 19 (1):37-40.
Richard B. White (1979). The Consistency of the Axiom of Comprehension in the Infinite-Valued Predicate Logic of Łukasiewicz. Journal of Philosophical Logic 8 (1):509 - 534.
Citations of this work BETA
Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.
David Ripley (2013). Paradoxes and Failures of Cut. Australasian Journal of Philosophy 91 (1):139 - 164.
Edwin Mares (2012). Relevant Logic and the Philosophy of Mathematics. Philosophy Compass 7 (7):481-494.
Alan Weir (2013). A Robust Non-Transitive Logic. Topoi 34 (1):1-9.
Zach Weber (2012). Transfinite Cardinals in Paraconsistent Set Theory. Review of Symbolic Logic 5 (2):269-293.
Similar books and articles
André Fuhrmann & Sven Ove Hansson (1994). A Survey of Multiple Contractions. Journal of Logic, Language and Information 3 (1):39-75.
Susan Rogerson & Sam Butchart (2002). Naïve Comprehension and Contracting Implications. Studia Logica 71 (1):119-132.
John K. Slaney (1984). A Metacompleteness Theorem for Contraction-Free Relevant Logics. Studia Logica 43 (1-2):159 - 168.
Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.
Roy Dyckhoff & Sara Negri (2000). Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic. Journal of Symbolic Logic 65 (4):1499-1518.
Raghav Ramachandran, Abhaya C. Nayak & Mehmet A. Orgun (2012). Three Approaches to Iterated Belief Contraction. Journal of Philosophical Logic 41 (1):115-142.
Rajeev Gore, Errata to Cambridge Computer Laboratory Technical Report Number 257: Cut-Free Sequent and Tableau Systems for Propositional Normal Modal Logics By.
Eiji Kiriyama & Hlroakira Ono (1991). The Contraction Rule and Decision Problems for Logics Without Structural Rules. Studia Logica 50 (2):299 - 319.
Sven Ove Hansson (2010). Multiple and Iterated Contraction Reduced to Single-Step Single-Sentence Contraction. Synthese 173 (2):153 - 177.
Added to index2009-01-28
Total downloads4 ( #289,040 of 1,410,150 )
Recent downloads (6 months)1 ( #177,743 of 1,410,150 )
How can I increase my downloads?