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124 lines
2.9 KiB
Python
124 lines
2.9 KiB
Python
"""
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Modeling the logic R
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"""
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from logic import (
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PropositionalVariable,
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Rule,
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Logic,
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Implication,
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Conjunction,
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Negation,
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Disjunction,
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Rule,
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)
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from model import Model, ModelFunction, ModelValue
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from generate_model import generate_model
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# ===================================================
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# Defining the logic of R
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x = PropositionalVariable("x")
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y = PropositionalVariable("y")
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z = PropositionalVariable("z")
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implication_rules = {
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Rule(set(), Implication(x, x)),
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Rule({Implication(x, y), Implication(y, z)}, Implication(x, z)),
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Rule({Implication(x, Implication(x, y)),}, Implication(x, y)),
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Rule({Implication(x, Implication(y, z)),}, Implication(y, Implication(x, z))),
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Rule({Implication(x, y),}, Implication(Implication(z, x), Implication(z, y))),
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Rule({Implication(x, y),}, Implication(Implication(y, z), Implication(x, z))),
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Rule({Implication(x, y), x}, y)
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}
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negation_rules = {
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Rule({Negation(Negation(x)),}, x),
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Rule({x,}, Negation(Negation(x))),
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Rule({Implication(x, y)}, Implication(Negation(y), Negation(x))),
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Rule({Implication(x, y),}, Implication(Negation(y), Negation(x)))
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}
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conjunction_rules = {
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Rule({y, z}, Conjunction(y, z)),
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Rule({Conjunction(x, y),}, x),
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Rule({Conjunction(x, y),}, y),
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Rule({Conjunction(Implication(x, y), Implication(x, z)),}, Implication(x, Conjunction(y, z)))
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}
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disjunction_rules = {
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Rule({x,}, Disjunction(x, y)),
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Rule({y,}, Disjunction(x, y)),
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Rule({Conjunction(Implication(x, z), Implication(y, z)),}, Implication(Disjunction(x, y), z)),
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Rule({Conjunction(x, Disjunction(y, z)),}, Disjunction(Conjunction(x, y), Conjunction(x, z)))
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}
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logic_rules = implication_rules | negation_rules | conjunction_rules | disjunction_rules
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operations = {Negation, Conjunction, Disjunction, Implication}
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R_logic = Logic(operations, logic_rules)
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# ===============================
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# Example Model of R
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a0 = ModelValue("a0")
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a1 = ModelValue("a1")
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carrier_set = {a0, a1}
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mnegation = ModelFunction({
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a0: a1,
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a1: a0
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})
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mimplication = ModelFunction({
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(a0, a0): a1,
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(a0, a1): a1,
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(a1, a0): a0,
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(a1, a1): a1
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})
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mconjunction = ModelFunction({
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(a0, a0): a0,
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(a0, a1): a0,
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(a1, a0): a0,
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(a1, a1): a1
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})
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mdisjunction = ModelFunction({
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(a0, a0): a0,
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(a0, a1): a1,
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(a1, a0): a1,
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(a1, a1): a1
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})
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designated_values = {a1}
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logical_operations = {
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mnegation, mimplication, mconjunction, mdisjunction
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}
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R_model_2 = Model(carrier_set, logical_operations, designated_values)
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interpretation = {
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Negation: mnegation,
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Conjunction: mconjunction,
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Disjunction: mdisjunction,
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Implication: mimplication
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}
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# =================================
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# Generate models of R of a given size
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model_size = 2
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satisfiable_models = generate_model(R_logic, model_size, print_model=True)
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print(f"There are {len(satisfiable_models)} satisfiable models of element length {model_size}")
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