On conjectures in orthocomplemented lattices
Artificial Intelligence
Consequences and conjectures in preordered sets
Information Sciences: an International Journal
A note on a deductive scheme of Dummett in classical and fuzzy logics
Fuzzy Sets and Systems
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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∧ defined in [4]. 2. Having shown that there is reason to consider the set C∧(P) of consequences of a set of premises P as too large, it is proven that C∧(P) is the largest set of consequences that can be assigned to P by means of a Tarski's consequences operator, provided that L is a Boolean algebra. 3. On the other hand, it is proven that, also in a Boolean algebra, the set Φ∧(P) of strict conjectures is the smallest of any Φ(P) such that P ⊆ Φ(P) and th at if P ⊆ Q then Φ(Q) ⊆ Φ(P).