Introduced ordering at model level...

This commit is contained in:
Brandon Rozek 2024-04-21 12:15:24 -04:00
parent 20ccacc166
commit ae8658fda2
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GPG key ID: 26E457DA82C9F480
2 changed files with 67 additions and 22 deletions

View file

@ -22,7 +22,7 @@ def possible_functions(operation, carrier_set):
new_function = dict()
for input, output in zip(inputs, outputs):
new_function[input] = output
yield ModelFunction(new_function, operation.symbol)
@ -46,7 +46,6 @@ def only_rules_with(rules: Set[Rule], operation: Operation) -> Set[Rule]:
return result_rules
def possible_interpretations(
logic: Logic, carrier_set: Set[ModelValue],
designated_values: Set[ModelValue]):
@ -88,10 +87,25 @@ def possible_interpretations(
yield interpretation
def generate_model(logic: Logic, number_elements: int, num_solutions: int = -1, print_model=False):
assert number_elements > 0
carrier_set = {
ModelValue("a" + str(i)) for i in range(number_elements)
}
ordering = set()
# a(0) is less than all other elements
a0 = ModelValue("a0")
for v in carrier_set:
if v != a0:
ordering.add(a0 < v)
# Every other element is less than a(n - 1)
an = ModelValue(f"a{number_elements-1}")
for v in carrier_set:
if an != v:
ordering.add(v < an)
possible_designated_values = possible_designations(carrier_set)
satisfied_models = []
@ -102,7 +116,7 @@ def generate_model(logic: Logic, number_elements: int, num_solutions: int = -1,
for interpretation in possible_interps:
is_valid = True
model = Model(carrier_set, set(interpretation.values()), designated_values)
model = Model(carrier_set, set(interpretation.values()), designated_values, ordering)
# Iteratively test possible interpretations
# by adding one axiom at a time
for rule in logic.rules:
@ -110,12 +124,12 @@ def generate_model(logic: Logic, number_elements: int, num_solutions: int = -1,
if not satisfiable(small_logic, model, interpretation):
is_valid = False
break
if is_valid:
satisfied_models.append(model)
if print_model:
print(model, flush=True)
if num_solutions >= 0 and len(satisfied_models) >= num_solutions:
return satisfied_models

View file

@ -5,8 +5,8 @@ from common import set_to_str
from logic import (
PropositionalVariable, get_propostional_variables, Logic, Term,
Operation
)
from typing import Set, List, Dict, Tuple
)
from typing import Set, List, Dict, Tuple, Optional
from itertools import product
from functools import lru_cache
@ -27,6 +27,9 @@ class ModelValue:
return self.hashed_value
def __eq__(self, other):
return isinstance(other, ModelValue) and self.name == other.name
def __lt__(self, other):
assert isinstance(other, ModelValue)
return ModelOrderConstraint(self, other)
class ModelFunction:
@ -42,9 +45,9 @@ class ModelFunction:
corrected_mapping[tuple(k)] = v
else: # Assume it's atomic
corrected_mapping[(k,)] = v
self.mapping = corrected_mapping
def __str__(self):
str_dict = dict()
for k, v in self.mapping.items():
@ -54,29 +57,44 @@ class ModelFunction:
def __call__(self, *args):
return self.mapping[args]
# def __eq__(self, other):
# return isinstance(other, ModelFunction) and self.name == other.name and self.arity == other.arity
class ModelOrderConstraint:
# a < b
def __init__(self, a: ModelValue, b: ModelValue):
self.a = a
self.b = b
def __hash__(self):
return hash(self.a) * hash(self.b)
def __eq__(self, other):
return isinstance(other, ModelOrderConstraint) and \
self.a == other.a and self.b == other.b
class Model:
def __init__(
self,
carrier_set: Set[ModelValue],
logical_operations: Set[ModelFunction],
designated_values: Set[ModelValue]
designated_values: Set[ModelValue],
ordering: Optional[Set[ModelOrderConstraint]] = None
):
assert designated_values <= carrier_set
self.carrier_set = carrier_set
self.logical_operations = logical_operations
self.designated_values = designated_values
self.ordering = ordering if ordering is not None else set()
# TODO: Make sure ordering is "valid"
# That is: transitive, etc.
def __str__(self):
result = f"""Carrier Set: {set_to_str(self.carrier_set)}
Designated Values: {set_to_str(self.designated_values)}
"""
for function in self.logical_operations:
result += f"{str(function)}\n"
return result
@ -89,13 +107,13 @@ def evaluate_term(t: Term, f: Dict[PropositionalVariable, ModelValue], interpret
for logic_arg in t.arguments:
model_arg = evaluate_term(logic_arg, f, interpretation)
model_arguments.append(model_arg)
return model_function(*model_arguments)
def all_model_valuations(
pvars: Tuple[PropositionalVariable],
mvalues: Tuple[ModelValue]):
possible_valuations = [mvalues for _ in pvars]
all_possible_values = product(*possible_valuations)
@ -116,20 +134,33 @@ def satisfiable(logic: Logic, model: Model, interpretation: Dict[Operation, Mode
pvars = tuple(get_propostional_variables(tuple(logic.rules)))
mappings = all_model_valuations_cached(pvars, tuple(model.carrier_set))
"""
TODO: Make sure that ordering for conjunction and disjunction
at the model function level.
"""
for mapping in mappings:
for rule in logic.rules:
premise_met = True
premise_ts = set()
for premise in rule.premises:
t = evaluate_term(premise, mapping, interpretation)
if t not in model.designated_values:
premise_t = evaluate_term(premise, mapping, interpretation)
if premise_t not in model.designated_values:
premise_met = False
break
premise_ts.add(premise_t)
if not premise_met:
continue
t = evaluate_term(rule.conclusion, mapping, interpretation)
if t not in model.designated_values:
consequent_t = evaluate_term(rule.conclusion, mapping, interpretation)
if consequent_t not in model.designated_values:
return False
# Make sure ordering constraint is met
for premise_t in premise_ts:
if consequent_t < premise_t in model.ordering:
return False
return True