That was fun! Thanks.

#!/usr/bin/perl -l

# http://perlmonks.org/?node_id=1209857

use strict;
use warnings;

$_ = <<END; # starting conditions
John apples,cherries,pears blacksmith,fisherman,programmer
Patrick apples,cherries,pears blacksmith,fisherman,programmer
Edward apples,cherries,pears blacksmith,fisherman,programmer
END

my $prev;
do
  {
  print;
  $prev = $_;

  s/^John \S*\Kpears//m;               # John doesn't like pears
  s/^Patrick \S+ \K\S+/blacksmith/m;   # Patrick is a blacksmith
  s/^Edward \S+ \S*\Kfisherman//m;     # Edward isn't a fisherman
  s/\S+(?= programmer$)/cherries/m;    # The programmer likes cherries

  s/,+\K,|\B,+|,+\B//g;                # cleanup extra commas

  for my $col (1 .. tr/ // / tr/\n// ) # for each column
    {
    for my $one ( /^(?:\S+ ){$col}(\w+)\s/gm ) # find each single one
      {
      s/^(?:\S+ ){$col}(?:\K$one,|\S+\K,$one\b)//gm; # delete in other
+ rows
      }
    }
  } until $_ eq $prev;
[download]

Outputs:

John apples,cherries,pears blacksmith,fisherman,programmer
Patrick apples,cherries,pears blacksmith,fisherman,programmer
Edward apples,cherries,pears blacksmith,fisherman,programmer

John apples,cherries fisherman,programmer
Patrick apples,cherries,pears blacksmith
Edward apples,cherries,pears programmer

John apples fisherman
Patrick apples,pears blacksmith
Edward cherries programmer

John apples fisherman
Patrick pears blacksmith
Edward cherries programmer
[download]