Natural Deduction for Two Connexive Logics.

I propose two natural-deduction proof-systems N ¬r and N ¬l, for non- classical interactions of a certain kind between negation and implication, that can be seen as variants of connexive logics. These interactions are inspired by a certain use of negation and implication in natural language. I propose the natural-deduction systems as meaning-conferring proof-systems, not appealing to any many-valued model theory as a semantics. The model-theory is used mainly as an auxiliary tool for establishing non-derivability, for example of some classical formal theorems (or, more generally, classical derivability claims) that are not provable (not derivable) in N ¬r and N ¬l. The relation between implication and negation in the system N ¬r is similar to the one by Cantwell and one by Cooper, the former unaware of the latter. The system N ¬l seems to be new.

Authors

• Nissim Francez

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