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123 lines
4.2 KiB
Python
123 lines
4.2 KiB
Python
"""
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Check to see if the model has the variable
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sharing property.
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"""
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from itertools import product
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from typing import List, Optional, Set, Tuple
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from common import set_to_str
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from model import (
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Model, model_closure, ModelFunction, ModelValue
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)
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class VSP_Result:
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def __init__(
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self, has_vsp: bool, model_name: Optional[str] = None,
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subalgebra1: Optional[Set[ModelValue]] = None,
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subalgebra2: Optional[Set[ModelValue]] = None):
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self.has_vsp = has_vsp
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self.model_name = model_name
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self.subalgebra1 = subalgebra1
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self.subalgebra2 = subalgebra2
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def __str__(self):
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if not self.has_vsp:
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return f"Model {self.model_name} does not have the variable sharing property."
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return f"""Model {self.model_name} has the variable sharing property.
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Subalgebra 1: {set_to_str(self.subalgebra1)}
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Subalgebra 2: {set_to_str(self.subalgebra2)}
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"""
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def has_vsp(model: Model, impfunction: ModelFunction,
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negation_defined: bool) -> VSP_Result:
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"""
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Checks whether a model has the variable
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sharing property.
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"""
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# NOTE: No models with only one designated
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# value satisfies VSP
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if len(model.designated_values) == 1:
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return VSP_Result(False, model.name)
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assert model.ordering is not None, "Expected ordering table in model"
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top = model.ordering.top()
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bottom = model.ordering.bottom()
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# Compute I the set of tuples (x, y) where
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# x -> y does not take a designiated value
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I: List[Tuple[ModelValue, ModelValue]] = []
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for (x, y) in product(model.carrier_set, model.carrier_set):
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if impfunction(x, y) not in model.designated_values:
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I.append((x, y))
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# Find the subalgebras which falsify implication
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for xys in I:
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xi = xys[0]
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# Discard ({⊥} ∪ A', B) subalgebras
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if bottom is not None and xi == bottom:
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continue
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# Discard ({⊤} ∪ A', B) subalgebras when negation is defined
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if top is not None and negation_defined and xi == top:
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continue
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yi = xys[1]
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# Discard (A, {⊤} ∪ B') subalgebras
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if top is not None and yi == top:
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continue
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# Discard (A, {⊥} ∪ B') subalgebras when negation is defined
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if bottom is not None and negation_defined and yi == bottom:
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continue
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# Discard ({a} ∪ A', {b} ∪ B') subalgebras when a <= b
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if model.ordering.is_lt(xi, yi):
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continue
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# Discard ({a} ∪ A', {b} ∪ B') subalgebras when b <= a and negation is defined
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if negation_defined and model.ordering.is_lt(yi, xi):
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continue
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# Compute the left closure of the set containing xi under all the operations
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carrier_set_left: Set[ModelValue] = model_closure({xi,}, model.logical_operations, bottom)
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# Discard ({⊥} ∪ A', B) subalgebras
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if bottom is not None and bottom in carrier_set_left:
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continue
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# Discard ({⊤} ∪ A', B) subalgebras when negation is defined
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if top is not None and negation_defined and top in carrier_set_left:
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continue
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# Compute the closure of all operations
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# with just the ys
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carrier_set_right: Set[ModelValue] = model_closure({yi,}, model.logical_operations, top)
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# Discard (A, {⊤} ∪ B') subalgebras
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if top is not None and top in carrier_set_right:
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continue
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# Discard (A, {⊥} ∪ B') subalgebras when negation is defined
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if bottom is not None and negation_defined and bottom in carrier_set_right:
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continue
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# Discard subalgebras that intersect
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if not carrier_set_left.isdisjoint(carrier_set_right):
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continue
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# Check whether for all pairs in the subalgebra,
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# that implication is falsified.
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falsified = True
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for (x2, y2) in product(carrier_set_left, carrier_set_right):
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if impfunction(x2, y2) in model.designated_values:
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falsified = False
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break
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if falsified:
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return VSP_Result(True, model.name, carrier_set_left, carrier_set_right)
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return VSP_Result(False, model.name)
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