MHB Working with decidable predicates

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The discussion revolves around understanding the calculation of decidable predicates as presented in a specific article. The main focus is on clarifying the first equation, which is not clearly numbered or formatted as an equation in the text. Participants express confusion about how to interpret the formula, particularly regarding its output being either 1 or 0. The lack of clarity in the article's presentation is a significant concern for those trying to grasp the concepts. Overall, the need for better formatting and explanation of the equations is emphasized.
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I am currently reading this article

Here

I was wondering how to calculate the contents of it
Mainly the first equation equaling 1 or 0
 
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This article does not seem to have numbered equations, and the first formula on its own line is not an equation.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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