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Deductive Logic to Inductive Logic
Notational Algebra & Symbolic Programming
Deductive – What | Inductive – Why, How
Deductive:- Statistical Summary of the Population by each Variable Recorded
Deductive:- Statistical Distribution of a Variable
Deductive:- Partitioning Data into Clusters
Cluster analysis is an unsupervised learning technique used for classification of data. Data elements are partitioned into groups called clusters that represent proximate collections of data elements based on a distance or dissimilarity function. Identical element pairs have zero distance or dissimilarity, and all others have positive distance or dissimilarity.
A correlation coefficient is a coefficient that illustrates a quantitative measure of some type of correlation and dependence, meaning statistical relationships between two or more random variables or observed data values.
The regression equation can be thought of as a mathematical model for a relationship between the two variables. The natural question is how good is the model, how good is the fit. That is where r comes in, the correlation coefficient (technically Pearson’s correlation coefficient for linear regression).
Inductive :- Hyperbolic Dirac Net
Notes on Synthesis of Forms :-
Christopher Alexander on Inductive Logic
The search for causal relations of this sort cannot be mechanically experimental or statistical; it requires interpretation: to practice it we must adopt the same kind of common sense that we have to make use of all the time in the inductive part of science. The data of scientific method never go further than to display regularities. We put structure into them only by inference and interpretation. In just the same way, the structural facts about a system of variables in an ensemble will come only from the thoughtful interpretation of observations.
But, in speaking of logic, we do not need to be concerned with processes of inference at all. While it is true that a great deal of what is generally understood to be logic is concerned with deduction, logic, in the widest sense, refers to something far more general . It is concerned with the form of abstract structures, and is involved the moment we make pictures of reality and then seek to manipulate these pictures so that we may look further into the reality itself . It is the business of logic to invent purely artificial structures of elements and relations.
Christopher Alexander:- Sometimes one of these structures is close enough to a real situation to be allowed to represent it. And then, because the logic is so tightly drawn, we gain insight into the reality which was previously withheld from us.