# -*- 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(K3.Meta):
name = 'K3W'
title = 'Weak Kleene Logic'
description = 'Three-valued logic with values T, F, and N'
category_order = 7
extension_of = ('K3WQ') # proof?
class Model(FDE.Model):
class TruthFunction(FDE.Model.TruthFunction):
def Conjunction(self, a, b, /):
if self.values.N in (a, b):
return self.values.N
return super().Conjunction(a, b)
def Disjunction(self, a, b, /):
if self.values.N in (a, b):
return self.values.N
return super().Disjunction(a, b)
class System(FDE.System): pass
[docs]
class Rules(LogicType.Rules):
closure = K3.Rules.closure
[docs]
class ConjunctionNegatedDesignated(System.OperatorNodeRule):
"""
From an unticked, designated, negated conjunction node *n* on a branch *b*, make
three new branches *b'*, *b''*, and *b'''* from *b*. On *b'* add a designated
node with the first conjunct, and a designated node with the negation of the
second conjunct. On *b''* add a designated node with the negation of the first
conjunct, and a designated node with the second conjunct. On *b'''* add
designated nodes with the negation of each conjunct. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(( lhs, True, w), (~rhs, True, w)),
sdwgroup((~lhs, True, w), ( rhs, True, w)),
sdwgroup((~lhs, True, w), (~rhs, True, w)))
[docs]
class ConjunctionNegatedUndesignated(System.OperatorNodeRule):
"""
From an unticked, undesignated, negated conjunction node *n* on a branch *b*, make
three new branches *b'*, *b''*, and *b'''* from *b*. On *b'* add undesignated nodes
for the first conjunct and its negation. On *b''* add undesignated nodes for the
second conjunct and its negation. On *b'''* add a designated node for each conjunct.
Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup((lhs, False, w), (~lhs, False, w)),
sdwgroup((rhs, False, w), (~rhs, False, w)),
sdwgroup((lhs, True, w), ( rhs, True, w)))
[docs]
class DisjunctionDesignated(System.OperatorNodeRule):
"""
From an unticked, designated, disjunction node *n* on a branch *b*, make
three new branches *b'*, *b''*, and *b'''* from *b*. On *b'* add a designated
node with the first disjunct, and a designated node with the negation of the
second disjunct. On *b''* add a designated node with the negation of the first
disjunct, and a designated node with the second disjunct. On *b'''* add a
designated node with each disjunct. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(( lhs, True, w), (~rhs, True, w)),
sdwgroup((~lhs, True, w), ( rhs, True, w)),
sdwgroup(( lhs, True, w), ( rhs, True, w)))
[docs]
class DisjunctionUndesignated(System.OperatorNodeRule):
"""
From an unticked, undesignated disjunction node *n* on a branch *b*, make three
new branches *b'*, *b''*, and *b'''* from b. On *b'* add undesignated nodes for
the first disjunct and its negation. On *b''* add undesignated nodes for the
second disjunct and its negation. On *b'''* add designated nodes for the negation
of each disjunct. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(( lhs, False, w), (~lhs, False, w)),
sdwgroup(( rhs, False, w), (~rhs, False, w)),
sdwgroup((~lhs, True, w), (~rhs, True, w)))
[docs]
class DisjunctionNegatedUndesignated(System.OperatorNodeRule):
"""
Either the disjunction is designated, or at least one of the disjuncts
has the value V{N}. So, from an unticked, undesignated, negated
disjunction node *n* on a branch *b*, make three branches *b'*, *b''*,
and *b'''* from *b*. On *b'* add a designated node with the disjunction.
On *b''* add two undesignated nodes with the first disjunct and its
negation, respectively. On *b'''* add undesignated nodes with the second
disjunct and its negation, respectively. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
yield adds(
sdwgroup((s, True, w)),
sdwgroup((s.lhs, False, w), (~s.lhs, False, w)),
sdwgroup((s.rhs, False, w), (~s.rhs, False, w)))
[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
[docs]
class ConditionalDesignated(System.MaterialConditionalReducingRule): pass
[docs]
class ConditionalNegatedDesignated(System.MaterialConditionalReducingRule): pass
[docs]
class ConditionalUndesignated(System.MaterialConditionalReducingRule): pass
[docs]
class ConditionalNegatedUndesignated(MaterialConditionalNegatedUndesignated): pass
[docs]
class BiconditionalDesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalNegatedDesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalUndesignated(System.MaterialConditionalConjunctsReducingRule): pass
[docs]
class BiconditionalNegatedUndesignated(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.DisjunctionNegatedDesignated,
FDE.Rules.ExistentialNegatedDesignated,
FDE.Rules.ExistentialNegatedUndesignated,
FDE.Rules.UniversalNegatedDesignated,
FDE.Rules.UniversalNegatedUndesignated,
FDE.Rules.DoubleNegationDesignated,
FDE.Rules.DoubleNegationUndesignated,
# reduction rules (thus, non-branching)
MaterialConditionalDesignated,
MaterialConditionalUndesignated,
MaterialConditionalNegatedDesignated,
MaterialConditionalNegatedUndesignated,
ConditionalDesignated,
ConditionalUndesignated,
ConditionalNegatedDesignated,
ConditionalNegatedUndesignated,
MaterialBiconditionalDesignated,
MaterialBiconditionalUndesignated,
MaterialBiconditionalNegatedDesignated,
MaterialBiconditionalNegatedUndesignated,
BiconditionalDesignated,
BiconditionalUndesignated,
BiconditionalNegatedDesignated,
BiconditionalNegatedUndesignated),
group(
# two-branching rules
FDE.Rules.ConjunctionUndesignated),
group(
# three-branching rules
DisjunctionDesignated,
DisjunctionUndesignated,
ConjunctionNegatedDesignated,
ConjunctionNegatedUndesignated,
# five-branching rules (formerly)
DisjunctionNegatedUndesignated),
# quantifier rules
*FDE.Rules.unquantifying_groups)
@classmethod
def _check_groups(cls):
for branching, group in zip(range(3), cls.groups):
for rulecls in group:
assert rulecls.branching == branching, f'{rulecls}'