Revistes Catalanes amb Accés Obert (RACO)

An orthogonality-based classification of conjectures in ortholattices

Enric Trillas i Gay, Ana Pradera Gómez


[Reviewed by Vinayak V. Joshi]-
-In the present paper, the authors prove results regarding the orthogonality of the elements of the set of strict conjectures with $p_{\wedge}$ in ortholattices; their results may be summarized as follows:

1. The only conjectures which are always left-orthogonal to $p_{\wedge}$ are consequences, whereas hypotheses are the only ones which are always right-orthogonal. But in the case of orthomodular lattices, consequences and hypotheses both are orthogonal to $p_{\wedge}$.

2. In general, it is possible to find conjectures of any kind (consequences, hypotheses or speculations of the two types) that are both left- and right-orthogonal to $p_{\wedge}$.

3. A conjecture that is neither left- nor right-orthogonal to $p_{\wedge}$ is necessarily a speculation.

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