×

Defining double negation elimination. (English) Zbl 0980.03033

Summary: In his paper “Generalized ortho negation” [in: H. Wansing (ed.), Negation. A notion in focus. Berlin: De Gruyter. Perspekt. Anal. Philos. 7, 3-26 (1996; Zbl 0979.03027)] J. Michael Dunn mentions a claim of mine to the effect that there is no condition on ‘perp frames’ equivalent to the holding of double negation elimination \(\sim\sim A\vdash A\). That claim is wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations which verify a number of different theses.

MSC:

03B60 Other nonclassical logic
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)

Citations:

Zbl 0979.03027
PDFBibTeX XMLCite
Full Text: DOI