General plans regarding the first article of MG and OK on logical data analysis.
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Detailed Description
General plans regarding the first article of MG and OK on logical data analysis.
The Latex file is DataAnalysis_MGOK1.tex
 Todo:
 General content

This article shall lay the foundations of boolean data analysis (boolean QCA), in a mathematical style.

Only the boolean side, while for the other aspects we refer to future articles.

Also with a presentation of the basic axioms (not mathematical) of QCA (for example "no randomness"), but in a succinct way.

Also with discussions of major issues from the literature (like the Lieberson/Ragin controversy), but again in a succinct way.

Of course we need examples, but they are only discussed as far as the illustration of the general method is concerned.

It needs also a historical section, where the historical development of QCA is outlined, with major publications.

Emphasis on precise definitions, especially giving semantical (non algorithmical) definitions of all concepts.

And emphasis on our framework for analysis of data, on the methods developed to investigate the "landscape of partial boolean functions".

We survey the existing algorithms (from the literature) for the given problems, but in this article no new algorithms are developed.

We also mention the OKlibrary, but are not concerned with implementations here.

We need to make statements about the computational complexity of all the basic tasks; here more work is needed.

We need also to link to the literature on machine learning; again, much more work is needed here.
 Todo:
 Title

"Foundations of logical data analysis for social sciences" would emphasise the generality of "logical data analysis".

"On the foundations of Qualitative Comparative Analysis (QCA)" would more bind us to the QCAmovement.

"On the foundations of Qualitative Comparative Analysis (QCA): Logical
data analysis for social sciences" would combine the two aspects.

"Social sciences" is too special; the main point here is the "qualitiave" aspect, that is, the high complexity involved, which leads to "boolean phenomena".

"On the foundations of Qualitative Comparative Analysis (QCA): Logical
data analysis for complex phenomena" perhaps is more appropriate.
 Todo:
 Journal

Discrete Applied Mathematics (DAM) has articles on logical data analysis and on heuristics.
 Todo:
 Structure

Section 1: Introduction

Perhaps 5 pages.

Explicitly stating that also the QCAaudience is addressed, and thus we have more basic explanations as usual.

Section 2: The history of QCA

Perhaps 5 pages.

Section 3: Basis notions for boolean logic

Perhaps 6 pages (because of examples and explanations).

Boolean functions, clausesets, CNF/DNF etc.

With explanations and examples, so that also the people from QCA have a chance.

Introducing our notions of "prime clauses" etc.

Section 4: The notion of a partial boolean function

Perhaps 7 pages (this is a very important concept).

We need an extensive literature review on partial boolean functions in the literature.

Here we also discuss the basics of the "relational" versus the "functional" point of view.

Section 5: On the axiomatic basis of QCA

Perhaps 5 pages (we could say much more, but not in this article, where we lay the foundations).

See chapter "Fundamental principles" in DataAnalysis.tex.

Section 6: The landscape of partial boolean functions

Perhaps 8 pages.

Here we present our methodology for the analysis of partial boolean functions.

Important to stress the duality between CNF and DNF.

Section 7: Incorporating aspects like temporality

Perhaps 4 pages.

Here we discuss how to translate various aspects into boolean logic.

Yet we only have the temporal aspects.

We also need to discuss the possibilities for translating nonboolean variables.

Section 8: On Randomness

Perhaps 5 pages.

Here the Lieberson/Ragin discussion with our solution of it.

Most basic then are notions of random partial boolean functions.

We need to make a full search for literature.

In various models of random partial boolean functions we present empirical results on how basic measures behave.

Section 9: Conclusions and outlook

Perhaps 4 pages.
 Todo:
 Create milestones
Definition in file DataAnalysis_MGOK1.hpp.