Models of Information Algebras
Here follows an incomplete list of instances of information algebras:
- Relational algebra: The reduct of a relational algebra with natural join as combination and the usual projection is a labeled information algebra, see Example.
- Constraint systems: Constraints form an information algebra (Jaffar & Maher 1994).
- Semiring valued algebras: C-Semirings induce information algebras (Bistarelli & Montanari Rossi1997);(Bistarelli et al. Schiex);(Kohlas & Wilson 2006).
- Logic: Many logic systems induce information algebras (Wilson & Mengin 1999). Reducts of cylindric algebras (Henkin, Monk & Tarski 1971) or polyadic algebras are information algebras related to predicate logic (Halmos 2000).
- Module algebras: (Bergstra, Heering & Klint 1990);(de Lavalette 1992).
- Linear systems: Systems of linear equations or linear inequalities induce information algebras (Kohlas 2003).
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