# Natural Language Toolkit: Interface to the Mace4 Model Builder
#
# Author: Dan Garrette <dhgarrette@gmail.com>
# Ewan Klein <ewan@inf.ed.ac.uk>
# URL: <http://nltk.org/>
# For license information, see LICENSE.TXT
"""
A model builder that makes use of the external 'Mace4' package.
"""
from __future__ import print_function
import os
import tempfile
from nltk.sem.logic import is_indvar
from nltk.sem import Valuation, Expression
from nltk.inference.api import ModelBuilder, BaseModelBuilderCommand
from nltk.inference.prover9 import Prover9CommandParent, Prover9Parent
[docs]class MaceCommand(Prover9CommandParent, BaseModelBuilderCommand):
"""
A ``MaceCommand`` specific to the ``Mace`` model builder. It contains
a print_assumptions() method that is used to print the list
of assumptions in multiple formats.
"""
_interpformat_bin = None
[docs] def __init__(self, goal=None, assumptions=None, max_models=500, model_builder=None):
"""
:param goal: Input expression to prove
:type goal: sem.Expression
:param assumptions: Input expressions to use as assumptions in
the proof.
:type assumptions: list(sem.Expression)
:param max_models: The maximum number of models that Mace will try before
simply returning false. (Use 0 for no maximum.)
:type max_models: int
"""
if model_builder is not None:
assert isinstance(model_builder, Mace)
else:
model_builder = Mace(max_models)
BaseModelBuilderCommand.__init__(self, model_builder, goal, assumptions)
@property
def valuation(mbc): return mbc.model('valuation')
def _convert2val(self, valuation_str):
"""
Transform the output file into an NLTK-style Valuation.
:return: A model if one is generated; None otherwise.
:rtype: sem.Valuation
"""
valuation_standard_format = self._transform_output(valuation_str, 'standard')
val = []
for line in valuation_standard_format.splitlines(False):
l = line.strip()
if l.startswith('interpretation'):
# find the number of entities in the model
num_entities = int(l[l.index('(')+1:l.index(',')].strip())
elif l.startswith('function') and l.find('_') == -1:
# replace the integer identifier with a corresponding alphabetic character
name = l[l.index('(')+1:l.index(',')].strip()
if is_indvar(name):
name = name.upper()
value = int(l[l.index('[')+1:l.index(']')].strip())
val.append((name, MaceCommand._make_model_var(value)))
elif l.startswith('relation'):
l = l[l.index('(')+1:]
if '(' in l:
#relation is not nullary
name = l[:l.index('(')].strip()
values = [int(v.strip()) for v in l[l.index('[')+1:l.index(']')].split(',')]
val.append((name, MaceCommand._make_relation_set(num_entities, values)))
else:
#relation is nullary
name = l[:l.index(',')].strip()
value = int(l[l.index('[')+1:l.index(']')].strip())
val.append((name, value == 1))
return Valuation(val)
@staticmethod
def _make_relation_set(num_entities, values):
"""
Convert a Mace4-style relation table into a dictionary.
:param num_entities: the number of entities in the model; determines the row length in the table.
:type num_entities: int
:param values: a list of 1's and 0's that represent whether a relation holds in a Mace4 model.
:type values: list of int
"""
r = set()
for position in [pos for (pos,v) in enumerate(values) if v == 1]:
r.add(tuple(MaceCommand._make_relation_tuple(position, values, num_entities)))
return r
@staticmethod
def _make_relation_tuple(position, values, num_entities):
if len(values) == 1:
return []
else:
sublist_size = len(values) // num_entities
sublist_start = position // sublist_size
sublist_position = int(position % sublist_size)
sublist = values[sublist_start*sublist_size:(sublist_start+1)*sublist_size]
return [MaceCommand._make_model_var(sublist_start)] + \
MaceCommand._make_relation_tuple(sublist_position,
sublist,
num_entities)
@staticmethod
def _make_model_var(value):
"""
Pick an alphabetic character as identifier for an entity in the model.
:param value: where to index into the list of characters
:type value: int
"""
letter = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n',
'o','p','q','r','s','t','u','v','w','x','y','z'][value]
num = value // 26
return (letter + str(num) if num > 0 else letter)
def _decorate_model(self, valuation_str, format):
"""
Print out a Mace4 model using any Mace4 ``interpformat`` format.
See http://www.cs.unm.edu/~mccune/mace4/manual/ for details.
:param valuation_str: str with the model builder's output
:param format: str indicating the format for displaying
models. Defaults to 'standard' format.
:return: str
"""
if not format:
return valuation_str
elif format == 'valuation':
return self._convert2val(valuation_str)
else:
return self._transform_output(valuation_str, format)
def _transform_output(self, valuation_str, format):
"""
Transform the output file into any Mace4 ``interpformat`` format.
:param format: Output format for displaying models.
:type format: str
"""
if format in ['standard', 'standard2', 'portable', 'tabular',
'raw', 'cooked', 'xml', 'tex']:
return self._call_interpformat(valuation_str, [format])[0]
else:
raise LookupError("The specified format does not exist")
def _call_interpformat(self, input_str, args=[], verbose=False):
"""
Call the ``interpformat`` binary with the given input.
:param input_str: A string whose contents are used as stdin.
:param args: A list of command-line arguments.
:return: A tuple (stdout, returncode)
:see: ``config_prover9``
"""
if self._interpformat_bin is None:
self._interpformat_bin = self._modelbuilder._find_binary(
'interpformat', verbose)
return self._modelbuilder._call(input_str, self._interpformat_bin,
args, verbose)
[docs]class Mace(Prover9Parent, ModelBuilder):
_mace4_bin = None
[docs] def __init__(self, end_size=500):
self._end_size = end_size
"""The maximum model size that Mace will try before
simply returning false. (Use -1 for no maximum.)"""
def _build_model(self, goal=None, assumptions=None, verbose=False):
"""
Use Mace4 to build a first order model.
:return: ``True`` if a model was found (i.e. Mace returns value of 0),
else ``False``
"""
if not assumptions:
assumptions = []
stdout, returncode = self._call_mace4(self.prover9_input(goal, assumptions),
verbose=verbose)
return (returncode == 0, stdout)
def _call_mace4(self, input_str, args=[], verbose=False):
"""
Call the ``mace4`` binary with the given input.
:param input_str: A string whose contents are used as stdin.
:param args: A list of command-line arguments.
:return: A tuple (stdout, returncode)
:see: ``config_prover9``
"""
if self._mace4_bin is None:
self._mace4_bin = self._find_binary('mace4', verbose)
updated_input_str = ''
if self._end_size > 0:
updated_input_str += 'assign(end_size, %d).\n\n' % self._end_size
updated_input_str += input_str
return self._call(updated_input_str, self._mace4_bin, args, verbose)
def spacer(num=30):
print('-' * num)
def decode_result(found):
"""
Decode the result of model_found()
:param found: The output of model_found()
:type found: bool
"""
return {True: 'Countermodel found', False: 'No countermodel found', None: 'None'}[found]
def test_model_found(arguments):
"""
Try some proofs and exhibit the results.
"""
for (goal, assumptions) in arguments:
g = Expression.fromstring(goal)
alist = [lp.parse(a) for a in assumptions]
m = MaceCommand(g, assumptions=alist, max_models=50)
found = m.build_model()
for a in alist:
print(' %s' % a)
print('|- %s: %s\n' % (g, decode_result(found)))
def test_build_model(arguments):
"""
Try to build a ``nltk.sem.Valuation``.
"""
g = Expression.fromstring('all x.man(x)')
alist = [Expression.fromstring(a) for a in ['man(John)',
'man(Socrates)',
'man(Bill)',
'some x.(-(x = John) & man(x) & sees(John,x))',
'some x.(-(x = Bill) & man(x))',
'all x.some y.(man(x) -> gives(Socrates,x,y))']]
m = MaceCommand(g, assumptions=alist)
m.build_model()
spacer()
print("Assumptions and Goal")
spacer()
for a in alist:
print(' %s' % a)
print('|- %s: %s\n' % (g, decode_result(m.build_model())))
spacer()
#print m.model('standard')
#print m.model('cooked')
print("Valuation")
spacer()
print(m.valuation, '\n')
def test_transform_output(argument_pair):
"""
Transform the model into various Mace4 ``interpformat`` formats.
"""
g = Expression.fromstring(argument_pair[0])
alist = [lp.parse(a) for a in argument_pair[1]]
m = MaceCommand(g, assumptions=alist)
m.build_model()
for a in alist:
print(' %s' % a)
print('|- %s: %s\n' % (g, m.build_model()))
for format in ['standard', 'portable', 'xml', 'cooked']:
spacer()
print("Using '%s' format" % format)
spacer()
print(m.model(format=format))
def test_make_relation_set():
print(MaceCommand._make_relation_set(num_entities=3, values=[1,0,1]) == set([('c',), ('a',)]))
print(MaceCommand._make_relation_set(num_entities=3, values=[0,0,0,0,0,0,1,0,0]) == set([('c', 'a')]))
print(MaceCommand._make_relation_set(num_entities=2, values=[0,0,1,0,0,0,1,0]) == set([('a', 'b', 'a'), ('b', 'b', 'a')]))
arguments = [
('mortal(Socrates)', ['all x.(man(x) -> mortal(x))', 'man(Socrates)']),
('(not mortal(Socrates))', ['all x.(man(x) -> mortal(x))', 'man(Socrates)'])
]
def demo():
test_model_found(arguments)
test_build_model(arguments)
test_transform_output(arguments[1])
if __name__ == '__main__':
demo()