Converse Ackermann Croperty and semiclassical negation

Méndez, José M.

doi:10.1007/bf00370290

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2006

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“…The problem concerning which systems do have the CAP is first posed in [1], §8.12 and in [7] it is solved for positive logics. Regarding negation, in [8], a so-called "semiclassical" negation and in [4], a strong negation are added to the positive logics in [7]. Finally, in [11] and [12] an intuitionistic negation is added to Intuitionistic and Dummett's LC positive logics with the CAP.…”

Section: Introductionmentioning

confidence: 99%

Converse Ackermann property and constructive negation defined with a negation connective

Robles

Méndez

2006

LLP

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The Converse Ackermann Property is the unprovability of formulas of the form (A → B) → C when C does contain neither → nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett's logic LC.

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