.. Copyright (C) 2001-2010 NLTK Project
.. For license information, see LICENSE.TXT

==================
Discourse Checking
==================

    >>> from nltk import *
    >>> from nltk.sem import logic
    >>> logic._counter._value = 0

Introduction
============

The NLTK discourse module makes it possible to test consistency and
redundancy of simple discourses, using theorem-proving and
model-building from `nltk.inference`.

The ``DiscourseTester`` constructor takes a list of sentences as a
parameter.

    >>> dt = DiscourseTester(['a boxer walks', 'every boxer chases a girl'])

The ``DiscourseTester`` parses each sentence into a list of logical
forms.  Once we have created ``DiscourseTester`` object, we can
inspect various properties of the discourse. First off, we might want
to double-check what sentences are currently stored as the discourse.

    >>> dt.sentences()
    s0: a boxer walks
    s1: every boxer chases a girl

As you will see, each sentence receives an identifier `s`\ :subscript:`i`.
We might also want to check what grammar the ``DiscourseTester`` is
using (by default, ``book_grammars/discourse.fcfg``):

    >>> dt.grammar() # doctest: +ELLIPSIS
    % start S
    # Grammar Rules
    S[SEM = <app(?subj,?vp)>] -> NP[NUM=?n,SEM=?subj] VP[NUM=?n,SEM=?vp]
    NP[NUM=?n,SEM=<app(?det,?nom)> ] -> Det[NUM=?n,SEM=?det]  Nom[NUM=?n,SEM=?nom]
    NP[LOC=?l,NUM=?n,SEM=?np] -> PropN[LOC=?l,NUM=?n,SEM=?np]
    ...

A different grammar can be invoked by using the optional ``gramfile``
parameter when a ``DiscourseTester`` object is created.

Readings and Threads
====================

Depending on
the grammar used, we may find some sentences have more than one
logical form. To check this, use the ``readings()`` method. Given a
sentence identifier of the form `s`\ :subscript:`i`, each reading of
that sentence is given an identifier `s`\ :sub:`i`-`r`\ :sub:`j`.


    >>> dt.readings()
    <BLANKLINE>
    s0 readings:
    <BLANKLINE>
    s0-r0: exists x.(boxer(x) & walk(x))
    s0-r1: exists x.(boxerdog(x) & walk(x))
    <BLANKLINE>
    s1 readings:
    <BLANKLINE>
    s1-r0: all x.(boxer(x) -> exists z1.(girl(z1) & chase(x,z1)))
    s1-r1: all x.(boxerdog(x) -> exists z2.(girl(z2) & chase(x,z2)))


In this case, the only source of ambiguity lies in the word *boxer*,
which receives two translations: ``boxer`` and ``boxerdog``. The
intention is that one of these corresponds to the ``person`` sense and
one to the ``dog`` sense. In principle, we would also expect to see a
quantifier scope ambiguity in ``s1``. However, the simple grammar we
are using, namely `sem4.fcfg <sem4.fcfg>`_, doesn't support quantifier
scope ambiguity.

We can also investigate the readings of a specific sentence:

    >>> dt.readings('a boxer walks')
    The sentence 'a boxer walks' has these readings:
        exists x.(boxer(x) & walk(x))
        exists x.(boxerdog(x) & walk(x))

Given that each sentence is two-ways ambiguous, we potentially have
four different discourse 'threads', taking all combinations of
readings. To see these, specify the ``threaded=True`` parameter on
the ``readings()`` method. Again, each thread is assigned an
identifier of the form `d`\ :sub:`i`. Following the identifier is a
list of the readings that constitute that thread.

    >>> dt.readings(threaded=True) # doctest: +NORMALIZE_WHITESPACE
    d0: ['s0-r0', 's1-r0']
    d1: ['s0-r0', 's1-r1']
    d2: ['s0-r1', 's1-r0']
    d3: ['s0-r1', 's1-r1']

Of course, this simple-minded approach doesn't scale: a discourse with, say, three
sentences, each of which has 3 readings, will generate 27 different
threads. It is an interesting exercise to consider how to manage
discourse ambiguity more efficiently.

Checking Consistency
====================

Now, we can check whether some or all of the discourse threads are
consistent, using the ``models()`` method. With no parameter, this
method will try to find a model for every discourse thread in the
current discourse. However, we can also specify just one thread, say ``d1``.

    >>> dt.models('d1')
    --------------------------------------------------------------------------------
    Model for Discourse Thread d1
    --------------------------------------------------------------------------------
    % number = 1
    % seconds = 0
    <BLANKLINE>
    % Interpretation of size 2
    <BLANKLINE>
    c1 = 0.
    <BLANKLINE>
    f1(0) = 0.
    f1(1) = 0.
    <BLANKLINE>
      boxer(0).
    - boxer(1).
    <BLANKLINE>
    - boxerdog(0).
    - boxerdog(1).
    <BLANKLINE>
    - girl(0).
    - girl(1).
    <BLANKLINE>
      walk(0).
    - walk(1).
    <BLANKLINE>
    - chase(0,0).
    - chase(0,1).
    - chase(1,0).
    - chase(1,1).
    <BLANKLINE>
    Consistent discourse: d1 ['s0-r0', 's1-r1']:
        s0-r0: exists x.(boxer(x) & walk(x))
        s1-r1: all x.(boxerdog(x) -> exists z8.(girl(z8) & chase(x,z8)))
    <BLANKLINE>

There are various formats for rendering **Mace4** models --- here,
we have used the 'cooked' format (which is intended to be
human-readable). There are a number of points to note.

#. The entities in the domain are all treated as non-negative
   integers. In this case, there are only two entities, ``0`` and
   ``1``.

#. The ``-`` symbol indicates negation. So ``0`` is the only
   ``boxerdog`` and the only thing that ``walk``\ s. Nothing is a
   ``boxer``, or a ``girl`` or in the ``chase`` relation. Thus the
   universal sentence is vacuously true.

#. ``c1`` is an introduced constant that denotes ``0``.

#. ``f1`` is a Skolem function, but it plays no significant role in
   this model.


We might want to now add another sentence to the discourse, and there
is method ``add_sentence()`` for doing just this.

    >>> dt.add_sentence('John is a boxer')
    >>> dt.sentences()
    s0: a boxer walks
    s1: every boxer chases a girl
    s2: John is a boxer

We can now test all the properties as before; here, we just show a
couple of them.

    >>> dt.readings()
    <BLANKLINE>
    s0 readings:
    <BLANKLINE>
    s0-r0: exists x.(boxer(x) & walk(x))
    s0-r1: exists x.(boxerdog(x) & walk(x))
    <BLANKLINE>
    s1 readings:
    <BLANKLINE>
    s1-r0: all x.(boxer(x) -> exists z9.(girl(z9) & chase(x,z9)))
    s1-r1: all x.(boxerdog(x) -> exists z10.(girl(z10) & chase(x,z10)))
    <BLANKLINE>
    s2 readings:
    <BLANKLINE>
    s2-r0: boxer(John)
    s2-r1: boxerdog(John)
    >>> dt.readings(threaded=True) # doctest: +NORMALIZE_WHITESPACE
    d0: ['s0-r0', 's1-r0', 's2-r0']
    d1: ['s0-r0', 's1-r0', 's2-r1']
    d2: ['s0-r0', 's1-r1', 's2-r0']
    d3: ['s0-r0', 's1-r1', 's2-r1']
    d4: ['s0-r1', 's1-r0', 's2-r0']
    d5: ['s0-r1', 's1-r0', 's2-r1']
    d6: ['s0-r1', 's1-r1', 's2-r0']
    d7: ['s0-r1', 's1-r1', 's2-r1']

If you are interested in a particular thread, the ``expand_threads()``
method will remind you of what readings it consists of:

    >>> thread = dt.expand_threads('d1')
    >>> for rid, reading in thread:
    ...     print rid, str(reading)
    s0-r0 exists x.(boxer(x) & walk(x))
    s1-r0 all x.(boxer(x) -> exists z11.(girl(z11) & chase(x,z11)))
    s2-r1 boxerdog(John)

Suppose we have already defined a discourse, as follows:

    >>> dt = DiscourseTester(['A student dances', 'Every student is a person'])

Now, when we add a new sentence, is it consistent with what we already
have? The `` consistchk=True`` parameter of ``add_sentence()`` allows
us to check:

    >>> dt.add_sentence('No person dances', consistchk=True)
    Inconsistent discourse: d0 ['s0-r0', 's1-r0', 's2-r0']:
        s0-r0: exists x.(student(x) & dance(x))
        s1-r0: all x.(student(x) -> person(x))
        s2-r0: -exists x.(person(x) & dance(x))
    <BLANKLINE>
    >>> dt.readings()
    <BLANKLINE>
    s0 readings:
    <BLANKLINE>
    s0-r0: exists x.(student(x) & dance(x))
    <BLANKLINE>
    s1 readings:
    <BLANKLINE>
    s1-r0: all x.(student(x) -> person(x))
    <BLANKLINE>
    s2 readings:
    <BLANKLINE>
    s2-r0: -exists x.(person(x) & dance(x))

So let's retract the inconsistent sentence:

    >>> dt.retract_sentence('No person dances', verbose=True) # doctest: +NORMALIZE_WHITESPACE
    Current sentences are 
    s0: A student dances
    s1: Every student is a person

We can now verify that result is consistent.

    >>> dt.models()
    --------------------------------------------------------------------------------
    Model for Discourse Thread d0
    --------------------------------------------------------------------------------
    % number = 1
    % seconds = 0
    <BLANKLINE>
    % Interpretation of size 2
    <BLANKLINE>
    c1 = 0.
    <BLANKLINE>
      dance(0).
    - dance(1).
    <BLANKLINE>
      person(0).
    - person(1).
    <BLANKLINE>
      student(0).
    - student(1).
    <BLANKLINE>
    Consistent discourse: d0 ['s0-r0', 's1-r0']:
        s0-r0: exists x.(student(x) & dance(x))
        s1-r0: all x.(student(x) -> person(x))
    <BLANKLINE>

Checking Informativity
======================

Let's assume that we are still trying to extend the discourse *A
student dances.* *Every student is a person.* We add a new sentence,
but this time, we check whether it is informative with respect to what
has gone before.

    >>> dt.add_sentence('A person dances', informchk=True)
    Sentence 'A person dances' under reading 'exists x.(person(x) & dance(x))':
    Not informative relative to thread 'd0'

In fact, we are just checking whether the new sentence is entailed by
the preceding discourse.

    >>> dt.models()
    --------------------------------------------------------------------------------
    Model for Discourse Thread d0
    --------------------------------------------------------------------------------
    % number = 1
    % seconds = 0
    <BLANKLINE>
    % Interpretation of size 2
    <BLANKLINE>
    c1 = 0.
    <BLANKLINE>
    c2 = 0.
    <BLANKLINE>
      dance(0).
    - dance(1).
    <BLANKLINE>
      person(0).
    - person(1).
    <BLANKLINE>
      student(0).
    - student(1).
    <BLANKLINE>
    Consistent discourse: d0 ['s0-r0', 's1-r0', 's2-r0']:
        s0-r0: exists x.(student(x) & dance(x))
        s1-r0: all x.(student(x) -> person(x))
        s2-r0: exists x.(person(x) & dance(x))
    <BLANKLINE>



Adding Background Knowledge
===========================

Let's build a new discourse, and look at the readings of the component sentences:

    >>> dt = DiscourseTester(['Vincent is a boxer', 'Fido is a boxer', 'Vincent is married', 'Fido barks'])
    >>> dt.readings()
    <BLANKLINE>
    s0 readings:
    <BLANKLINE>
    s0-r0: boxer(Vincent)
    s0-r1: boxerdog(Vincent)
    <BLANKLINE>
    s1 readings:
    <BLANKLINE>
    s1-r0: boxer(Fido)
    s1-r1: boxerdog(Fido)
    <BLANKLINE>
    s2 readings:
    <BLANKLINE>
    s2-r0: married(Vincent)
    <BLANKLINE>
    s3 readings:
    <BLANKLINE>
    s3-r0: bark(Fido)

This gives us a lot of threads:

    >>> dt.readings(threaded=True) # doctest: +NORMALIZE_WHITESPACE
    d0: ['s0-r0', 's1-r0', 's2-r0', 's3-r0']
    d1: ['s0-r0', 's1-r1', 's2-r0', 's3-r0']
    d2: ['s0-r1', 's1-r0', 's2-r0', 's3-r0']
    d3: ['s0-r1', 's1-r1', 's2-r0', 's3-r0']


We can eliminate some of the readings, and hence some of the threads,
by adding background information.

    >>> import nltk.data
    >>> bg = nltk.data.load('grammars/book_grammars/background.fol')
    >>> dt.add_background(bg)
    >>> dt.background()
    all x.(boxerdog(x) -> dog(x))
    all x.(boxer(x) -> person(x))
    all x.-(dog(x) & person(x))
    all x.(married(x) <-> exists y.marry(x,y))
    all x.(bark(x) -> dog(x))
    all x y.(marry(x,y) -> (person(x) & person(y)))
    -(Vincent = Mia)
    -(Vincent = Fido)
    -(Mia = Fido)

The background information allows us to reject three of the threads as
inconsistent. To see what remains, use the ``filter=True`` parameter
on ``readings()``.

    >>> dt.readings(filter=True) # doctest: +NORMALIZE_WHITESPACE
    d1: ['s0-r0', 's1-r1', 's2-r0', 's3-r0']

The ``models()`` method gives us more information about the surviving thread.

    >>> dt.models()
    --------------------------------------------------------------------------------
    Model for Discourse Thread d0
    --------------------------------------------------------------------------------
    No model found!
    <BLANKLINE>
    --------------------------------------------------------------------------------
    Model for Discourse Thread d1
    --------------------------------------------------------------------------------
    % number = 1
    % seconds = 0
    <BLANKLINE>
    % Interpretation of size 3
    <BLANKLINE>
    Fido = 0.
    <BLANKLINE>
    Mia = 1.
    <BLANKLINE>
    Vincent = 2.
    <BLANKLINE>
    f1(0) = 0.
    f1(1) = 0.
    f1(2) = 2.
    <BLANKLINE>
      bark(0).
    - bark(1).
    - bark(2).
    <BLANKLINE>
    - boxer(0).
    - boxer(1).
      boxer(2).
    <BLANKLINE>
      boxerdog(0).
    - boxerdog(1).
    - boxerdog(2).
    <BLANKLINE>
      dog(0).
    - dog(1).
    - dog(2).
    <BLANKLINE>
    - married(0).
    - married(1).
      married(2).
    <BLANKLINE>
    - person(0).
    - person(1).
      person(2).
    <BLANKLINE>
    - marry(0,0).
    - marry(0,1).
    - marry(0,2).
    - marry(1,0).
    - marry(1,1).
    - marry(1,2).
    - marry(2,0).
    - marry(2,1).
      marry(2,2).
    <BLANKLINE>
    --------------------------------------------------------------------------------
    Model for Discourse Thread d2
    --------------------------------------------------------------------------------
    No model found!
    <BLANKLINE>
    --------------------------------------------------------------------------------
    Model for Discourse Thread d3
    --------------------------------------------------------------------------------
    No model found!
    <BLANKLINE>
    Inconsistent discourse: d0 ['s0-r0', 's1-r0', 's2-r0', 's3-r0']:
        s0-r0: boxer(Vincent)
        s1-r0: boxer(Fido)
        s2-r0: married(Vincent)
        s3-r0: bark(Fido)
    <BLANKLINE>
    Consistent discourse: d1 ['s0-r0', 's1-r1', 's2-r0', 's3-r0']:
        s0-r0: boxer(Vincent)
        s1-r1: boxerdog(Fido)
        s2-r0: married(Vincent)
        s3-r0: bark(Fido)
    <BLANKLINE>
    Inconsistent discourse: d2 ['s0-r1', 's1-r0', 's2-r0', 's3-r0']:
        s0-r1: boxerdog(Vincent)
        s1-r0: boxer(Fido)
        s2-r0: married(Vincent)
        s3-r0: bark(Fido)
    <BLANKLINE>
    Inconsistent discourse: d3 ['s0-r1', 's1-r1', 's2-r0', 's3-r0']:
        s0-r1: boxerdog(Vincent)
        s1-r1: boxerdog(Fido)
        s2-r0: married(Vincent)
        s3-r0: bark(Fido)
    <BLANKLINE>


..  This will not be visible in the html output: create a tempdir to
    play in.
    >>> import tempfile, os
    >>> tempdir = tempfile.mkdtemp()
    >>> old_dir = os.path.abspath('.')
    >>> os.chdir(tempdir)

In order to play around with your own version of background knowledge,
you might want to start off with a local copy of ``background.fol``:

    >>> nltk.data.retrieve('grammars/book_grammars/background.fol')
    Retrieving 'grammars/book_grammars/background.fol', saving to 'background.fol'

After you have modified the file, the ``parse_logic()`` function will parse 
the strings in the file into expressions of ``nltk.logic``.

    >>> from nltk.inference.discourse import parse_fol
    >>> mybg = parse_fol(open('background.fol').read())

The result can be loaded as an argument of ``add_background()`` in the
manner shown earlier.

..  This will not be visible in the html output: clean up the tempdir.
    >>> os.chdir(old_dir)
    >>> for f in os.listdir(tempdir):
    ...     os.remove(os.path.join(tempdir, f))
    >>> os.rmdir(tempdir)
    >>> nltk.data.clear_cache()


Regression Testing from book
============================

    >>> logic._counter._value = 0

    >>> from nltk.tag import RegexpTagger
    >>> tagger = RegexpTagger(
    ...     [('^(chases|runs)$', 'VB'),
    ...      ('^(a)$', 'ex_quant'),
    ...      ('^(every)$', 'univ_quant'),
    ...      ('^(dog|boy)$', 'NN'),
    ...      ('^(He)$', 'PRP')
    ... ])
    >>> rc = DrtGlueReadingCommand(depparser=MaltParser(tagger=tagger))
    >>> dt = DiscourseTester(['Every dog chases a boy', 'He runs'], rc)
    >>> dt.readings()
    <BLANKLINE>
    s0 readings:
    <BLANKLINE>
    s0-r0: ([],[(([x],[dog(x)]) -> ([z1],[boy(z1), chases(x,z1)]))])
    s0-r1: ([z2],[boy(z2), (([x],[dog(x)]) -> ([],[chases(x,z2)]))])
    <BLANKLINE>
    s1 readings:
    <BLANKLINE>
    s1-r0: ([x],[PRO(x), runs(x)])
    >>> dt.readings(show_thread_readings=True)
    d0: ['s0-r0', 's1-r0'] : INVALID: AnaphoraResolutionException
    d1: ['s0-r1', 's1-r0'] : ([z6,z10],[boy(z6), (([x],[dog(x)]) -> ([],[chases(x,z6)])), (z10 = z6), runs(z10)])
    >>> dt.readings(filter=True, show_thread_readings=True)
    d1: ['s0-r1', 's1-r0'] : ([z12,z15],[boy(z12), (([x],[dog(x)]) -> ([],[chases(x,z12)])), (z15 = z12), runs(z15)])

    >>> from nltk.parse import load_earley
    >>> from nltk.sem.drt import DrtParser
    >>> parser = load_earley('grammars/book_grammars/drt.fcfg', trace=0, logic_parser=DrtParser())
    >>> trees = parser.nbest_parse('Angus owns a dog'.split())
    >>> print trees[0].node['SEM'].simplify()
    ([x,z17],[Angus(x), dog(z17), own(x,z17)])
