Converse Ackermann property and constructive negation defined with a negation connective

Gemma Robles, José M. Méndez

DOI: http://dx.doi.org/10.12775/LLP.2006.007

Abstract


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.

Keywords


converse Ackermann property, constructive negation, relational ternary semantics, Relevance logics

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References


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