[FOM] Why inclusive disjunction?

[Neil Tennant]

On Wed, 10 Jan 2007, Richard Heck wrote:

> [A]re there introduction and elimination rules for exclusive or that
> don't involve other connectives?

Yes.

Neil Tennant
______________________________________________________

[#: absurdity sign]

	  (i)__   __(i)	    (i)__   __(i)
	      A , B	        A , B
Intro	        :		  :
	A       #	   B      #
	__________(i)	   _________(i)
	  A aut B	    A aut B

[In the relevant logics CR and IR, specify that in applications
of the first half of aut-Intro, the assumption B must be used; and
that in applications of the second half of aut-Intro, the assumption A
must be used.]

  		(i)__  	 __(i)
Elim		    A    B
		    :	 :
	A aut B     C    C	  A aut B    A     B
	___________________(i)    __________________
		    C		           #

[In the relevant logics CR and IR, specify that in applications
of the first half of aut-Elim, the assumption A must be used in
the first case-proof, and the assumption B must be used in the second
case-proof.]