The axioms belonging in the Foundation Domain are used to steer the theory (which includes the Laws of the science); the Theory Domain steers the Methodology Domain, which steers the Applications. The observations made in the Domain of Applications are fed into the Foundation Domain, namely the Axioms and the language of the science, and modify them accordingly.

In the case of Euclidean geometry, Euclid was playing in the sand of the Aegean sea, when he discovered his geometry. He conjectured four axioms, such as you can draw from a point only one parallel line to another line. Euclid was able to deduce from these four axioms all the laws and theorems of his geometry. The Euclidean geometry was very instrumental for the discovery of classical (Newtonian) mechanics in the 18th century; it became irrelevant, however, for relativistic mechanics and the General Theory of Relativity (GTR) invented by Einstein in the 20th century. GTR was founded on the axioms of Riemannian geometry, and not the axioms of the Euclidean geometry. All geometries are axiomatic, and so is the Archanesian geometry of Dialogic Design Science.

The graphic language patterns of the Archanesian geometry, shown below, are used by the stakeholders in Co-Laboratories of Democracy to construct translatable graphics relevant to their specific social system designing situation:

Image of Steps in Each Stage of Inquiry

= Some Graphic Patterns of the Observation Types of the Archanesian Geometry are shown below:

Seven Language Patterns(Years 1970-1989):## (1) Elemental observation,

(2)Problematique,(3) Influence tree pattern,(4) Options field pattern,(5) Options profile/scenario pattern,(6) Superposition pattern, and(7) Action plan pattern## The meaning assigned to Axioms in the DDS is the equivalent of the meaning of Postulates assigned by Warfield in the Domain of Science Model (DOSM):

## The axioms belonging in the Foundation Domain are used to steer the theory (which includes the Laws of the science); the Theory Domain steers the Methodology Domain, which steers the Applications. The observations made in the Domain of Applications are fed into the Foundation Domain, namely the Axioms and the language of the science, and modify them accordingly.

## In the case of Euclidean geometry, Euclid was playing in the sand of the Aegean sea, when he discovered his geometry. He conjectured four axioms, such as you can draw from a point only one parallel line to another line. Euclid was able to deduce from these four axioms all the laws and theorems of his geometry. The Euclidean geometry was very instrumental for the discovery of classical (Newtonian) mechanics in the 18th century; it became irrelevant, however, for relativistic mechanics and the General Theory of Relativity (GTR) invented by Einstein in the 20th century. GTR was founded on the axioms of Riemannian geometry, and not the axioms of the Euclidean geometry. All geometries are axiomatic, and so is the Archanesian geometry of Dialogic Design Science.

## The graphic language patterns of the Archanesian geometry, shown below, are used by the stakeholders in Co-Laboratories of Democracy to construct translatable graphics relevant to their specific social system designing situation:

=

Some Graphic Patterns of the Observation Types of the Archanesian Geometry are shown below:

=