Lattice-theoretic models of conjectures, hypotheses and consequences

摘要

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.