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As the analysis progresses, theory emerges both inductively and deductively [26].
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However, they also considered an alternative simpler definition according to which the progressed theory is always first-order definable.
They conjectured that this alternative definition is incorrect in the sense that the progressed theory is too weak and may sometimes lose information.
First, we prove the Lin and Reiter conjecture by presenting a case where the progressed theory indeed does lose information, thus closing a question that has remained open for more than ten years.
They also showed that this definition comes with a strong negative result, namely that for certain cases first-order logic is not expressive enough to correctly characterize the progressed theory and second-order axioms are necessary.
The interplay between inductive and deductive procedures in IPA means that as the analysis progresses existing theory can be endorsed, modified, and/or challenged.
Further progress in theory, implementation and computational performance is desirable.
All of these implementations are interwoven with the progress in theory and applications.
Recent progress, in theory and a tremendous increase in computer power, has fundamentally changed this situation.
Recent progress in theory, psychophysics, and neurophysiology indicate that cortical circuitry might meet these challenges by evaluating sensory signals probabilistically.
Karl Poppers explains progress in theory development by falsification [14], Thomas Kuhn explains revolutions in research by changing paradigms [39], and Imre Lakatos describes progress in research as rational group behaviour [3, 12, 40].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com