On the reducibility of hypotheses and consequences

This paper only tries to shed some additional light on the concepts of hypotheses and consequences, introduced by Trillas et al. [E. Trillas, S. Cubillo, and E. Castiñeira, On conjectures in orthocomplemented lattices, Artificial Intelligence, 117 (2) (2000) 255-275] as particular cases of the more general concept of conjecture. The definitions of reducible hypothesis and reducible consequence are presented, and it is shown that in orthomodular lattices all hypotheses and consequences are reducible, but that this is not necessarily the case in proper ortholattices. In addition, the sets of reducible hypotheses and consequences are characterized, both for general ortholattices as well as for the particular case of orthomodular lattices.