Information Algebras

  • Jürg Kohlas
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)


On several occasions we encountered idempotent valuation algebras. In the labeled version this means that
$$ \varphi \otimes \varphi ^{ \downarrow t} = \varphi $$
whenever \( t \subseteq d\left( \varphi \right) \). This a very appealing property. In fact, if a valuation φ represents some piece of information about a domain d(φ) = s, then its marginal \( \varphi ^{ \downarrow t} \) represents a part of φ. The idempotency says that combining a piece of information with a part of it, gives nothing new! This really is a property which is characteristic of information. We may repeat a piece of information as often as we want, we never get something new. That is why we call valuation algebras which possess the idempotency property an information algebra. The justification of this name will be later reinforced by other considerations (see Sections 6.2, 6.3 and 6.4 below).


Consequence Operator Finite Subset Relational Algebra Convex Polyhedron Linear Manifold 
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Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • Jürg Kohlas
    • 1
  1. 1.Department of InformaticsUniversity of FribourgFribourgSwitzerland

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