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Why definitions?

Definitions help assign specific meanings to terms applied in any domain. In the context of locational-state the purpose of this theory is to help decision-makers identify and collect all necessary information required to take a decision. In the discipline of decision analysis, a decision is defined as an irrevocable allocation of resources to a course of action. To avoid disappointments and wasted resources it is therefore necessary to make sure that the cause and effect relationships that are assumed to influence the results of decisions are correct and that all of the necessary information is available upon which to base the decision.

Invariably, decisions are taken on the basis of incomplete knowledge concerning cause and effect and therefore incomplete information. A considerable amount of scientific research concentrates on establishing specific relationships. However, effective decisions require an understanding of a broader range of relationships. Locational-state theory provides a domain of enquiry to manage the quest to establish the integration of multiple relationships and to specify the information required for decision-making.

The nature of the definitions on this page

The definitions on this page are stark in the sense they define a term while the examples of the application are to be found in the content of different sections on this site. Where the term is used, a link to this page is provided.

Decision analysis

Decisions are usually based on a conceptual model of reality. Each person has a different life experience, exposure to different information and as a result possess slightly different perceptions of the likelihood or events and levels of understanding of the associated processes that cause specific events. There will normally be differences in people's view on the implications of these events. As a result, people's conceptual models of reality differ. Therefore, when it comes to group decisions there is a need for all concerned to agree on the conceptual model being applied to determine the potential outcomes of each course of action linked to decision options.

Usually some basic facts can be agreed upon such as by applying more fertilizer crop yields will be higher. Starting with known facts it is then easier to add qualifying information which does not counter the commonly agreed facts. So the degree to which fertilizer increases yield depends upon water availability, soil texture and temperatures. The locational-state model is based on known facts but also includes all of the additional determinants that are linked to space-time, that influence the values and the effects of the properties of the commonly agreed determinants on the designed target property (yield).

Complete and incomplete data sets

A simple representation of the determinant model is given below where a desired State of a target property (Stp) is a determinate function (D()) of two determinants "a" and "b".

Stp = D(a,b) ... (i)

Subsequent research might establish that two additional determinants "c" and "d" also influence Stp. Therefore the new model is as follows:

Stp = D(a,b,c,d) ... (ii)

Clearly determinate function (ii) has a more complete data set that determinate function (i). However, this data set does not contain any locational-state properties and relationships and therefore it is still incomplete.

By adding longitude, latitude, altitude, chronological time and the age of the object that transforms determinants into a target property value e.g. crop yield, the result is a significant improvement in the precision of measurement of the correlation between determinant values and measured target property states. The implication of this statement is that many conceptual models or decision analysis models are not based on complete data sets and locational-state theory at the present time in human development (2020) can demonstrate this to be a fact.

Statistical significance

One important fact arising from the subject of complete and incomplete data sets is that with complete data sets that have been collected over a area of terrain or from year to year, the level of "unexplained variance" between data sets is far lower and comparable with "explained variance" within data sets. This signifies that complete data sets contains sufficient determinants to explain the state of the target properties in most location whereas an incomplete data set cannot achieve this. Therefore by using locational-state theory to specify more complete data sets, the statistical significance in terms of explaining property variations is greater.

State machines and locational-state models

In information technology, circuit and program design, the equivalent would be what is referred to as a "state machine". However, the difference between a "state machine" and a "locational-state model" is that in the case of the locational-state model the determinant states will normally change as a function of the object (system) location in three dimensional space (longitude, latitude and altitude) and with time. Time is measures as chronological time as well as the age of the object whose target property is being measured. For example a biomass yield of a crop can be represented as th following input-output identity of the :

Stp = D(W,T,N,P,K,E,H,G) ... (iii)
Where:

Stp is the State of the target property, or output, in this case biomass;
D id the determinate function which includes the following inputs as determinants:
W is the water regime;
T is the temperature regime;
N is the available nitrogen applied;
P is the available phosphorus applied;
K is the available potassium applied
E is the energy used e.g. liquid fuels
H is the human resources used
G is the genotype (variety) and quantity of seed used.



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