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