This paper is a brief continuation of earlier work by the same authors [4] and [5] that deals with the concepts of conjecture, hypothesis and consequence in orthocomplemented complete lattices. It considers only the following three points: 1. Classical logic theorems of both deduction and contradiction are reinterpreted and proved by means of one specific operator C sub(∧) defined in [4]. 2. Having shown that there is reason to consider the set C sub(∧)(P) of consequences of a set of premises as too large, it is proven that C sub(∧)(P) is the largest set of consequences that can be assigned to by means of a Tarski's consequences operator, provided that is a Boolean algebra. 3. On the other hand, it is proven that, also in a Boolean algebra, the set Фsub(∧)(P) of strict conjectures is the smallest of any Ф (P) such that and that P is contained in Ф (P) if P is contained in Q thenФsub(∧)(Q) is contained in Ф (P).
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