Information Algebra - Axioms and Definition

Axioms and Definition

The axioms of the two-sorted algebra, in addition to the axioms of the lattice :

Semigroup
is a commutative semigroup under combination with a neutral element (representing vacuous information).
Distributivity of Focusing over Combination

To focus an information on combined with another information to domain, one may as well first focus the second information to and combine then.

Transitivity of Focusing

To focus an information on and, one may focus it to .

Idempotency

An information combined with a part of itself gives nothing new.

Support
such that

Each information refers to at least one domain (question).

A two-sorted algebra satisfying these axioms is called an Information Algebra.

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