Abstract
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. © 2002 Elsevier Science B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 253-267 |
| Journal | Artificial Intelligence |
| Volume | 139 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Aug 2002 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
The first author was supported by the National Science Foundation for Distinguished Young Scholars (Grant No: 69725004), Key Project for Basic Researches (Grant No: 1998030509) and Natural Sciences Foundation (Grant No: 69823001) of China.
Research Keywords
- Conjecture
- Consequence
- Hypothesis
- Orthocomplemented lattice
- Residuated lattice
- Uncertain reasoning
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