having all the rules of Hilbert’s positive logic (cf. for example [3, p. 98]), the connective of negation ¬ is said to be conditional iff ` ⊆ |=M, where |=M is the consequence relation determined on L by a model M =< I,≤, φ, A > (with a nonempty partially ordered set < I,≤>, a valuation φ ⊆ I × V , V is the set of propositional variables, and A ⊆ I, ∅ 6= A 6= I) in the standard way: for any X ⊆...