Converse Ackermann property and constructive negation defined with a negation connective | Zendy

Gemma Robles | Zendy; José M. Méndez | Zendy

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Converse Ackermann property and constructive negation defined with a negation connective

Author(s) -

Gemma Robles,

José M. Méndez

Publication year - 2006

Publication title -

logic and logical philosophy

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.416

H-Index - 10

eISSN - 2300-9802

pISSN - 1425-3305

DOI - 10.12775/llp.2006.007

Subject(s) - converse , negation , ackermann function , property (philosophy) , mathematics , constructive , pure mathematics , logical consequence , discrete mathematics , algebra over a field , calculus (dental) , linguistics , computer science , philosophy , epistemology , programming language , inverse , geometry , process (computing) , medicine , dentistry

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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