Philosophy Lexicon of Arguments

Quantifiers: in the predicate logic, quantifiers are the symbol combinations (Ex) and (x) for the set of objects to which one or more properties are attributed to. A) Existence quantification (Ex)(Fx) ("At least one x"). B) Universal quantification (x)(Fx) ("Everything is F"). For other objects e.g. y, z,… are chosen. E.g. (x) (Ey) (Fx > Gy). See also quantification, generalized quantifiers.
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I 28
Branched quantifiers/branching/stronger/weaker/Hintikka:
Example branching here:
1st branch: There is an x and b knows ...
2nd branch: b knows there is an x ...
Quantification with branched quantifiers is extremely strong, almost as strong as 2nd level logic.
Therefore, it cannot be completely axiomatized. (Quantified epistemic logic with unlimited independence).
I 29
Variant: a variant would refer to simpler cases where the independence refers to ignorance, combined with a move with a single, un-negated, non-epistemic operator {b} K. Here, an explicit treatment is possible.

Hin I
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989

J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996

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Ed. Martin Schulz, access date 2017-05-22