# -*- coding: utf-8 -*-
# pytableaux, a multi-logic proof generator.
# Copyright (C) 2014-2023 Doug Owings.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from __future__ import annotations
from ..proof import adds, sdwgroup
from ..tools import group
from . import fde as FDE
from . import k3 as K3
from . import l3 as L3
from . import LogicType
class Meta(L3.Meta):
name = 'G3'
title = 'Gödel 3-valued Logic'
description = (
'Three-valued logic (T, F, N) with alternate '
'negation and conditional')
category_order = 10
class Model(FDE.Model):
class TruthFunction(L3.Model.TruthFunction):
def Negation(self, a, /):
if a == self.values.N:
return self.values.F
return super().Negation(a)
class System(FDE.System): pass
[docs]
class Rules(LogicType.Rules):
closure = K3.Rules.closure
[docs]
class ConditionalNegatedDesignated(System.OperatorNodeRule):
"""
From an unticked, designated, negated conditional node `n` on a branch
`b`, make two branches `b'` and `b''` from `b`. On `b'` add two designated
nodes, one with the antecedent, and one with the negation of the consequent.
On `b''` add two undesignated nodes, one with the antecedent, and one with
the negation of the antecedent, and one designated node with the negation
of the consequent. Then tick `n`.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(
( lhs, d, w),
(~rhs, d, w)),
sdwgroup(
( lhs, not d, w),
(~lhs, not d, w),
(~rhs, d, w)))
[docs]
class ConditionalNegatedUndesignated(System.OperatorNodeRule):
"""
From an unticked, undesignated, negated conditional node `n` on a branch
`b`, make two branches `b'` and `b''` from `b`. On `b'` add a designated
node with the negation of the antecedent. On `b''` add an undesignated
node with the negation of the consequent. Then tick `n`.
"""
def _get_sdw_targets(self, s, d, w, /):
yield adds(
sdwgroup((~s.lhs, not d, w)),
sdwgroup((~s.rhs, d, w)))
[docs]
class DoubleNegationDesignated(System.FlippingRule): pass
[docs]
class DoubleNegationUndesignated(System.FlippingRule): pass
[docs]
class BiconditionalDesignated(System.ConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalNegatedDesignated(System.ConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalUndesignated(System.ConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalNegatedUndesignated(System.ConditionalConjunctsReducingRule): pass
[docs]
class MaterialConditionalDesignated(System.MaterialConditionalReducingRule): pass
[docs]
class MaterialConditionalNegatedDesignated(System.MaterialConditionalReducingRule): pass
[docs]
class MaterialConditionalUndesignated(System.MaterialConditionalReducingRule): pass
[docs]
class MaterialConditionalNegatedUndesignated(System.MaterialConditionalReducingRule): pass
[docs]
class MaterialBiconditionalDesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class MaterialBiconditionalNegatedDesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class MaterialBiconditionalUndesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class MaterialBiconditionalNegatedUndesignated(System.MaterialConditionalConjunctsReducingRule): pass
groups = (
group(
# non-branching rules
FDE.Rules.AssertionDesignated,
FDE.Rules.AssertionUndesignated,
FDE.Rules.AssertionNegatedDesignated,
FDE.Rules.AssertionNegatedUndesignated,
FDE.Rules.ConjunctionDesignated,
FDE.Rules.ConjunctionNegatedUndesignated,
FDE.Rules.DisjunctionNegatedDesignated,
FDE.Rules.DisjunctionUndesignated,
FDE.Rules.ExistentialNegatedDesignated,
FDE.Rules.ExistentialNegatedUndesignated,
FDE.Rules.UniversalNegatedDesignated,
FDE.Rules.UniversalNegatedUndesignated,
DoubleNegationDesignated,
DoubleNegationUndesignated,
# reduction rules
MaterialConditionalNegatedDesignated,
MaterialConditionalUndesignated,
MaterialConditionalDesignated,
MaterialConditionalNegatedUndesignated,
MaterialBiconditionalDesignated,
MaterialBiconditionalNegatedDesignated,
MaterialBiconditionalUndesignated,
MaterialBiconditionalNegatedUndesignated,
BiconditionalDesignated,
BiconditionalNegatedUndesignated,
BiconditionalUndesignated,
BiconditionalNegatedDesignated),
group(
# branching rules
FDE.Rules.ConjunctionNegatedDesignated,
FDE.Rules.ConjunctionUndesignated,
FDE.Rules.DisjunctionDesignated,
FDE.Rules.DisjunctionNegatedUndesignated,
L3.Rules.ConditionalDesignated,
L3.Rules.ConditionalUndesignated,
ConditionalNegatedUndesignated,
ConditionalNegatedDesignated),
# quantifier rules
*FDE.Rules.groups[-2:])
@classmethod
def _check_groups(cls):
for branching, group in zip(range(2), cls.groups):
for rulecls in group:
assert rulecls.branching == branching, f'{rulecls}'