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)
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)
