Summary

We shall define minimal negation and a broad spectrum of subminimal negations within a number of subsystems of positive (negationless) intuitionistic logic. We understand "minimal negation" in its classical historical sense (Johansson, 1936). With "subminimal negation" we refer to any negation included in minimal negation.

In particular, we aim to show how to define minimal negation and a systematically defined set of subminimal negations in any logic including Sylvan's basic positive logic and included in the positive superintuitionistic logic LC.

In the first place, we shall define the forementioned negations by means of the introduction in the positive systems of a particular falsity constant. Then, if desired, it is possible to equivalently introduce a connective for negation. Finally, we modelize all the resulting logics with ternary relational semantics.

This project was based at the Universidad de Salamanca (Spain) and was funded by the Spanish Ministry of Science and Technology (MCYT) [grant no. BFF2001-2066]. It ran from 2001 till 2004.