How to be really contraction free

Greg Restall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


A logic is said to be contraction free if the rule from A → (A →B) to A →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 is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly 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.

Original languageEnglish
Pages (from-to)381-391
Number of pages11
JournalStudia Logica
Issue number3
Publication statusPublished - Sept 1993


Dive into the research topics of 'How to be really contraction free'. Together they form a unique fingerprint.

Cite this