Artificial Intelligence
Theoretical Computer Science
Fuzzifying topology based on complete residuated lattice-valued logic (I)
Fuzzy Sets and Systems
A logic for approximate reasoning
Journal of Symbolic Logic
Communications of the ACM
On conjectures in orthocomplemented lattices
Artificial Intelligence
Artificial Intelligence
Representation of occurrences for road vehicle traffic
Artificial Intelligence
On the reducibility of hypotheses and consequences
Information Sciences: an International Journal
Consequences and conjectures in preordered sets
Information Sciences: an International Journal
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Trillas, Cubillo and Castiñeira [Artificial Intelligence 117 (2000) 255-275] defined several interesting operators in orthocomplemented lattices. These operators give a quite general algebraic model for conjectures, consequences and hypotheses. We present some properties of conjectures, consequences and hypotheses in orthocomplemented lattices, which complement or improve the results by Trillas, Cubillo and Castiñeira. Furthermore, we introduce the graded versions of these notions in the setting of residuated lattices and derive some of their properties. These graded notions provide certain mathematical tools for modelling conjectures, consequences and hypotheses in the environment where uncertain and vague information is involved.