... the -I ev(N,X ,P[ X]) p[ x ]-1 ~-i X N -I ever)' -a sm(N,X ,P[ X]) p[ x ]-1 ~-i X N -1 some -x N -I tt(N,X ,P[ X]) p[ X] -I a -I X ~ that -I Figure 1 : A G-grammar for a fragment of English assumed ... -= A -1 r(A) saw -v A -I s(A,B) B -I in , E -I i(E,A) A -I the 7 t(N) N -I ever)' , o ev(N,X ,P[ X]) some , c~ sm(N,X ,P[ X]) that-v N -I tt(N,X ,P[ X]) p[ x]-I ~-I X N -I P[ X]-a ... of a group. We consider a com- patible preorder notated x -4 y on a group G. The fol- lowing properties, for any x, y E G, are immediate: x -+ y ¢:~ x y- l -4 1; x -4 y ¢0 y-l -4 x-1; x-41...