2015 Fiscal Year Final Research Report
On preservation of Stone-type dualities
| Project/Area Number |
24700017
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Fundamental theory of informatics
|
|---|
| Research Institution | Kanagawa University (2013-2015)
Tottori University of Environmental Studies (2012) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2016-03-31
|
| Keywords | 情報科学 / ストーン型双対性 / 多値論理 / 多重関係 / 表現定理 |
|---|
| Outline of Final Research Achievements |
Our goal is to give the sufficient condition for preservation of Stone-type dualities among different multi-valued logics. As a result, we gave the construction of the adjunction between the category of join semilattices over T-algebras and the category of complete join semilattices over T-algebras, by using the adjunction between the category of join semilattices and the category of complete join semilattices. We proved the relational representation theorem of quantales whose order and monoid structure are respectively given by inclusion and relational composition and the identity relation. As a similar example, we provided the multirelational representation theorem of complete idempotent left semirings. Finally, we defined the notion of multi-valued multirelations as a generalization of multirelations and multi-valued relations.
|
| Free Research Field |
情報科学
|
