[FOM] Why inclusive disjunction?

Stephen Pollard spollard at truman.edu
Thu Jan 11 09:47:28 EST 2007

Richard Heck asked:

> Are there introduction and elimination rules for exclusive or that  
> don't involve other connectives?

The Shoesmith/Smiley technique yields the axiomatization:

A,B,f(AB) =>
A => B,f(AB)
B => A,f(AB)
f(AB) => A,B

People who don't like multiple-conclusion logics can replace the last  
three principles with a separation of cases rule: pick any two of A,  
B, f(AB); if each of the ones you picked yield C, then so does the  
one you didn't pick.

Stephen Pollard
Professor of Philosophy
Division of Social Science
Truman State University
spollard at truman.edu

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