Name
Abstract | ||
|---|---|---|
We discuss completions of basic algebras. We prove that the ideal completion of a basic algebra is also a basic algebra. It
will be shown that basic algebras are not closed under MacNeille completions. By adding the join-infinite distributive law
to basic algebras, we will show that these kind of basic algebras are closed under the closed ideal completion and moreover
any other regular completions of these algebras are isomorphic to the closed ideal completion. As an application we establish
an algebraic completeness theorem for a logic weaker than Visser’s basic predicate logic, BQL, a proper subsystem of intuitionistic predicate logic, IQL.
|
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/978-3-642-02261-6_7 | Workshop on Logic, Language, Information and Computation |
Keywords | Field | DocType |
visser's basic logic,algebraic completeness theorem,join-infinite distributive law,ideal completion,proper subsystem,macneille completion,basic algebras,completion,basic predicate logic,intuitionistic logic.,heyting algebra,basic algebra,regular completion,closed ideal completion,intuitionistic predicate logic,distributive law,intuitionistic logic | Intuitionistic logic,Subalgebra,Interior algebra,Distributive property,Discrete mathematics,Algebra,Pure mathematics,Heyting algebra,Abstract algebraic logic,Predicate logic,Mathematics,Algebra representation | Conference |
Volume | ISSN | Citations |
5514 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 4 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Majid Alizadeh | 1 | 21 | 5.60 |