On conjectures in orthocomplemented lattices Original Research Article

A mathematical model for conjectures in orthocomplemented lattices is presented. After defining when a conjecture is a consequence or a hypothesis, some operators of conjectures, consequences and hypotheses are introduced and some properties they show are studied. This is the case, for example, of being monotonic or non-monotonic operators. As orthocomplemented lattices contain orthomodular lattices and Boolean algebras, they offer a sufficiently broad framework to obtain some general results that can be restricted to such particular, but important, lattices. This is, for example, the case of the structureʹs theorem for hypotheses. Some results are illustrated by examples of mathematical or linguistic character, and an appendix on orthocomplemented lattices is included.