[FOM], independent freindly logic

H. Enderton hbe at math.ucla.edu
Sat Dec 27 15:24:08 EST 2003

George Kapoulas wrote:
>2) There is an approach for logic called independent friendly logic.
>Does anyone know  if there is proof that the approach used by this
>logic  cannot be expressed in 1st order logic, and references for

What Hintikka calls independence-friendly (IF) logic is more often
called logic with "branching quantifiers."  Yes, it goes beyond 
first-order logic.  The proof (Ehrenfeucht's) appears in the first
paper on the subject, which was Henkin's paper in the Infinitistic
Methods volume (hence the name "Henkin quantifiers" which is also

Since that paper came out, there have been more results.  If nowhere
else, references to the early work can be found in my paper on this
in the Zeitschrift fuer math Logik, vol. 16 (1970), 393-397.

An interesting issue is how "natural" branching quantifiers are, and
in particular whether there are sentences in natural languages whose
symbolization requires branching quantifiers.  Barwise and other
linguists have looked at this.  That is, if symbolic logic is to
cover reasoning in natural languages, must it consequently incorporate
branching quantifiers?

--Herb Enderton

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