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So I'm still reading The GUHA Method of Automatic Hypothesis Determination by P. Hajek, and there he uses a phrase:

set of predicates with a determined form

I have no idea what determined form is. Searching doesn't help. Anyone can help?

I include the context of the phrase from the paper (see yellow underline):

determinedform

P.S.: For bibliography used in paper see my other question: What is L-implication?

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Andriy Drozdyuk
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    He means the predicates in $A \cup B \cup C$ - these are the ones whose form is "determined". As he says in the previous paragraph, not all predicates may be in that union. When something is written in parentheses like that, you can assume it is a restatement or elaboration on the other material of the same sentence. – Carl Mummert Jan 27 '16 at 12:49
  • @CarlMummert I believe you're right. Otherwise it makes no sense - because interesting applies to "disjunctions", and cannot be absolutely defined. This is simply for the definition of the "probe" (A,B,C, M,N) - relative to which the notion of interesting is applied. You should answer so I can accept. – Andriy Drozdyuk Jan 30 '16 at 03:25

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From context, it sounds like "a predicate with a determined form" just means "a predicate that is either interesting only if it is positive or interesting only if it is negative". That is, the "form" of a predicate is just whether it is positive or negative (which I assume refers to whether the predicate itself appears or whether its negation appears), and a predicate has a determined form if only one of its forms can occur in an "interesting" disjunction.

To put it another way, the term "determined form" has no prior meaning. When a probe $(A,B,C,M,N)$ has been chosen, the elements of $M$ are referred to as "of determined form" with respect to this probe. The term "determined" is used to describe the role of $M$ (and its subset $N$) in the definition of "interesting".

Eric Wofsey
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  • This is all before the "interesting" paragraph; it appears he only means the predicates in $A\cup B \cup C$. – Carl Mummert Jan 27 '16 at 12:50
  • As far as I can tell the only purpose of talking about $A\cup B\cup C$ is to define "interesting", and $M$ is specified to be a subset of $A\cup B\cup C$. – Eric Wofsey Jan 27 '16 at 18:30