102 lines
5.3 KiB
Python
102 lines
5.3 KiB
Python
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# Natural Language Toolkit: Semantic Interpretation
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#
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# Author: Ewan Klein <ewan@inf.ed.ac.uk>
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#
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# Copyright (C) 2001-2018 NLTK Project
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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from nltk.sem.logic import (AllExpression, AndExpression, ApplicationExpression,
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EqualityExpression, ExistsExpression, IffExpression,
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ImpExpression, NegatedExpression, OrExpression,
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VariableExpression, skolem_function, unique_variable)
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def skolemize(expression, univ_scope=None, used_variables=None):
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"""
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Skolemize the expression and convert to conjunctive normal form (CNF)
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"""
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if univ_scope is None:
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univ_scope = set()
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if used_variables is None:
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used_variables = set()
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if isinstance(expression, AllExpression):
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term = skolemize(expression.term, univ_scope|set([expression.variable]), used_variables|set([expression.variable]))
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return term.replace(expression.variable, VariableExpression(unique_variable(ignore=used_variables)))
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elif isinstance(expression, AndExpression):
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return skolemize(expression.first, univ_scope, used_variables) &\
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skolemize(expression.second, univ_scope, used_variables)
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elif isinstance(expression, OrExpression):
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return to_cnf(skolemize(expression.first, univ_scope, used_variables),
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skolemize(expression.second, univ_scope, used_variables))
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elif isinstance(expression, ImpExpression):
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return to_cnf(skolemize(-expression.first, univ_scope, used_variables),
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skolemize(expression.second, univ_scope, used_variables))
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elif isinstance(expression, IffExpression):
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return to_cnf(skolemize(-expression.first, univ_scope, used_variables),
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skolemize(expression.second, univ_scope, used_variables)) &\
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to_cnf(skolemize(expression.first, univ_scope, used_variables),
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skolemize(-expression.second, univ_scope, used_variables))
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elif isinstance(expression, EqualityExpression):
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return expression
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elif isinstance(expression, NegatedExpression):
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negated = expression.term
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if isinstance(negated, AllExpression):
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term = skolemize(-negated.term, univ_scope, used_variables|set([negated.variable]))
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if univ_scope:
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return term.replace(negated.variable, skolem_function(univ_scope))
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else:
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skolem_constant = VariableExpression(unique_variable(ignore=used_variables))
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return term.replace(negated.variable, skolem_constant)
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elif isinstance(negated, AndExpression):
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return to_cnf(skolemize(-negated.first, univ_scope, used_variables),
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skolemize(-negated.second, univ_scope, used_variables))
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elif isinstance(negated, OrExpression):
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return skolemize(-negated.first, univ_scope, used_variables) &\
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skolemize(-negated.second, univ_scope, used_variables)
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elif isinstance(negated, ImpExpression):
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return skolemize(negated.first, univ_scope, used_variables) &\
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skolemize(-negated.second, univ_scope, used_variables)
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elif isinstance(negated, IffExpression):
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return to_cnf(skolemize(-negated.first, univ_scope, used_variables),
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skolemize(-negated.second, univ_scope, used_variables)) &\
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to_cnf(skolemize(negated.first, univ_scope, used_variables),
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skolemize(negated.second, univ_scope, used_variables))
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elif isinstance(negated, EqualityExpression):
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return expression
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elif isinstance(negated, NegatedExpression):
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return skolemize(negated.term, univ_scope, used_variables)
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elif isinstance(negated, ExistsExpression):
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term = skolemize(-negated.term, univ_scope|set([negated.variable]), used_variables|set([negated.variable]))
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return term.replace(negated.variable, VariableExpression(unique_variable(ignore=used_variables)))
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elif isinstance(negated, ApplicationExpression):
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return expression
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else:
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raise Exception('\'%s\' cannot be skolemized' % expression)
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elif isinstance(expression, ExistsExpression):
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term = skolemize(expression.term, univ_scope, used_variables|set([expression.variable]))
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if univ_scope:
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return term.replace(expression.variable, skolem_function(univ_scope))
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else:
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skolem_constant = VariableExpression(unique_variable(ignore=used_variables))
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return term.replace(expression.variable, skolem_constant)
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elif isinstance(expression, ApplicationExpression):
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return expression
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else:
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raise Exception('\'%s\' cannot be skolemized' % expression)
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def to_cnf(first, second):
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"""
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Convert this split disjunction to conjunctive normal form (CNF)
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"""
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if isinstance(first, AndExpression):
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r_first = to_cnf(first.first, second)
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r_second = to_cnf(first.second, second)
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return r_first & r_second
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elif isinstance(second, AndExpression):
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r_first = to_cnf(first, second.first)
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r_second = to_cnf(first, second.second)
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return r_first & r_second
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else:
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return first | second
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