Summary

We understand "minimal negation" in its historical classical sense (Johansson, 1936). With "subminimal negation" we refer to any negation included in minimal negation. Ternary relational semantics are the semantics defined by Routley and Meyer in the early seventies of the past century. And finally, logics with the A.P. ("Ackermann Property") are entailment logics in Anderson and Belnap's sense.

In a very general way, we can split the purpose into three different aims: (a) To define the ninimal positive logic in which intuitionistic negation is definable. (b) To define the stronger constructive negation compatible with the A.P. (It has to be a subminimal negation). (c) To define the set of subminimal negations generated by the rules of double negation, contraposition and reductio in the basic positive logic of the ternary relational semantics.

This project was based at the Universidad de Salamanca (Spain) and was funded by the Spanish Ministry of Education and Science (MEC) [grant no. HUM2005-05707]. It ran from 2005 till 2008.