# -*- 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 ..lang import Operator
from ..proof import adds, sdwgroup
from ..tools import group
from . import fde as FDE
from . import l3 as L3
from . import lp as LP
from . import LogicType
class Meta(LP.Meta):
name = 'RM3'
title = 'R-mingle 3'
description = (
'Three-valued logic (True, False, Both) with a primitive '
'Conditional operator')
category_order = 6
native_operators = FDE.Meta.native_operators | (
Operator.Conditional,
Operator.Biconditional)
class Model(LP.Model):
class TruthFunction(FDE.Model.TruthFunction):
def Conditional(self, a, b):
if a > b:
return self.values.F
return super().Conditional(a, b)
class System(FDE.System): pass
[docs]
class Rules(LogicType.Rules):
closure = LP.Rules.closure
[docs]
class ConditionalDesignated(System.OperatorNodeRule):
"""
From an unticked, designated conditional node *n* on a branch *b*, make
three branches *b'*, *b''*, and *b'''* from *b*. On *b'* add an undesignated
node with the antecedent. On *b''* add an undesignated node with the
negation of the consequent. On *b'''* add four designated nodes, with
the antecedent, its negation, the consequent, and its negation,
respectively. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(( lhs, not d, w)),
sdwgroup((~rhs, not d, w)),
sdwgroup(
( lhs, d, w),
(~lhs, d, w),
( rhs, d, w),
(~rhs, d, w)))
[docs]
class ConditionalUndesignated(System.OperatorNodeRule):
"""
From an unticked, undesignated, conditional node *n* on a branch *b*, make
two branches *b'* and *b''* from *b*. On *b'*, add a designated node
with the antecedent, and an undesignated node with with consequent.
On *b''*, add an undesignated node with the negation of the antecedent,
and a designated 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),
( s.rhs, d, w)),
sdwgroup(
(~s.lhs, d, w),
(~s.rhs, not d, w)))
[docs]
class BiconditionalDesignated(System.OperatorNodeRule):
"""
From an unticked designated biconditional node *n* on a branch *b*, make
three branches *b'*, *b''*, and *b'''* from *b*. On *b'* add undesignated
nodes for each of the two operands. On *b''*, add undesignated nodes fo
the negation of each operand. On *b'''*, add four designated nodes, one
with each operand, and one for the negation of each operand. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
lhs, rhs = s
yield adds(
sdwgroup(
( lhs, not d, w),
( rhs, not d, w)),
sdwgroup(
(~lhs, not d, w),
(~rhs, not d, w)),
sdwgroup(
( lhs, d, w),
(~lhs, d, w),
( rhs, d, w),
(~rhs, d, w)))
[docs]
class BiconditionalNegatedUndesignated(System.OperatorNodeRule):
"""
From an unticked undesignated negated biconditional node *n* on a branch *b*,
make two branches *b'* and *b''* from *b*. On *b'* add an undesignated node
for each operand. On *b''* add an undesignated nodes for the negation of
each operand. Then tick *n*.
"""
def _get_sdw_targets(self, s, d, w, /):
yield adds(
sdwgroup(
(s.lhs, d, w),
(s.rhs, d, w)),
sdwgroup(
(~s.lhs, d, w),
(~s.rhs, d, w)))
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.MaterialConditionalNegatedDesignated,
FDE.Rules.MaterialConditionalUndesignated,
FDE.Rules.ConditionalNegatedDesignated,
FDE.Rules.ExistentialNegatedDesignated,
FDE.Rules.ExistentialNegatedUndesignated,
FDE.Rules.UniversalNegatedDesignated,
FDE.Rules.UniversalNegatedUndesignated,
FDE.Rules.DoubleNegationDesignated,
FDE.Rules.DoubleNegationUndesignated),
group(
# 2 branching rules
FDE.Rules.ConjunctionNegatedDesignated,
FDE.Rules.ConjunctionUndesignated,
FDE.Rules.DisjunctionDesignated,
FDE.Rules.DisjunctionNegatedUndesignated,
FDE.Rules.MaterialConditionalDesignated,
FDE.Rules.MaterialConditionalNegatedUndesignated,
FDE.Rules.MaterialBiconditionalDesignated,
FDE.Rules.MaterialBiconditionalNegatedDesignated,
FDE.Rules.MaterialBiconditionalUndesignated,
FDE.Rules.MaterialBiconditionalNegatedUndesignated,
ConditionalUndesignated,
FDE.Rules.ConditionalNegatedUndesignated,
FDE.Rules.BiconditionalNegatedDesignated,
L3.Rules.BiconditionalUndesignated,
BiconditionalNegatedUndesignated),
group(
# 3 branching rules
ConditionalDesignated,
BiconditionalDesignated),
# 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}'