Source code for nltk.sem.skolemize

# Natural Language Toolkit: Semantic Interpretation
#
# Author: Ewan Klein <ewan@inf.ed.ac.uk>
#
# Copyright (C) 2001-2019 NLTK Project
# URL: <http://nltk.org/>
# For license information, see LICENSE.TXT

from nltk.sem.logic import (
    AllExpression,
    AndExpression,
    ApplicationExpression,
    EqualityExpression,
    ExistsExpression,
    IffExpression,
    ImpExpression,
    NegatedExpression,
    OrExpression,
    VariableExpression,
    skolem_function,
    unique_variable,
)


[docs]def skolemize(expression, univ_scope=None, used_variables=None): """ Skolemize the expression and convert to conjunctive normal form (CNF) """ if univ_scope is None: univ_scope = set() if used_variables is None: used_variables = set() if isinstance(expression, AllExpression): term = skolemize( expression.term, univ_scope | set([expression.variable]), used_variables | set([expression.variable]), ) return term.replace( expression.variable, VariableExpression(unique_variable(ignore=used_variables)), ) elif isinstance(expression, AndExpression): return skolemize(expression.first, univ_scope, used_variables) & skolemize( expression.second, univ_scope, used_variables ) elif isinstance(expression, OrExpression): return to_cnf( skolemize(expression.first, univ_scope, used_variables), skolemize(expression.second, univ_scope, used_variables), ) elif isinstance(expression, ImpExpression): return to_cnf( skolemize(-expression.first, univ_scope, used_variables), skolemize(expression.second, univ_scope, used_variables), ) elif isinstance(expression, IffExpression): return to_cnf( skolemize(-expression.first, univ_scope, used_variables), skolemize(expression.second, univ_scope, used_variables), ) & to_cnf( skolemize(expression.first, univ_scope, used_variables), skolemize(-expression.second, univ_scope, used_variables), ) elif isinstance(expression, EqualityExpression): return expression elif isinstance(expression, NegatedExpression): negated = expression.term if isinstance(negated, AllExpression): term = skolemize( -negated.term, univ_scope, used_variables | set([negated.variable]) ) if univ_scope: return term.replace(negated.variable, skolem_function(univ_scope)) else: skolem_constant = VariableExpression( unique_variable(ignore=used_variables) ) return term.replace(negated.variable, skolem_constant) elif isinstance(negated, AndExpression): return to_cnf( skolemize(-negated.first, univ_scope, used_variables), skolemize(-negated.second, univ_scope, used_variables), ) elif isinstance(negated, OrExpression): return skolemize(-negated.first, univ_scope, used_variables) & skolemize( -negated.second, univ_scope, used_variables ) elif isinstance(negated, ImpExpression): return skolemize(negated.first, univ_scope, used_variables) & skolemize( -negated.second, univ_scope, used_variables ) elif isinstance(negated, IffExpression): return to_cnf( skolemize(-negated.first, univ_scope, used_variables), skolemize(-negated.second, univ_scope, used_variables), ) & to_cnf( skolemize(negated.first, univ_scope, used_variables), skolemize(negated.second, univ_scope, used_variables), ) elif isinstance(negated, EqualityExpression): return expression elif isinstance(negated, NegatedExpression): return skolemize(negated.term, univ_scope, used_variables) elif isinstance(negated, ExistsExpression): term = skolemize( -negated.term, univ_scope | set([negated.variable]), used_variables | set([negated.variable]), ) return term.replace( negated.variable, VariableExpression(unique_variable(ignore=used_variables)), ) elif isinstance(negated, ApplicationExpression): return expression else: raise Exception('\'%s\' cannot be skolemized' % expression) elif isinstance(expression, ExistsExpression): term = skolemize( expression.term, univ_scope, used_variables | set([expression.variable]) ) if univ_scope: return term.replace(expression.variable, skolem_function(univ_scope)) else: skolem_constant = VariableExpression(unique_variable(ignore=used_variables)) return term.replace(expression.variable, skolem_constant) elif isinstance(expression, ApplicationExpression): return expression else: raise Exception('\'%s\' cannot be skolemized' % expression)
[docs]def to_cnf(first, second): """ Convert this split disjunction to conjunctive normal form (CNF) """ if isinstance(first, AndExpression): r_first = to_cnf(first.first, second) r_second = to_cnf(first.second, second) return r_first & r_second elif isinstance(second, AndExpression): r_first = to_cnf(first, second.first) r_second = to_cnf(first, second.second) return r_first & r_second else: return first | second