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Brandon Rozek 2024-05-29 13:50:20 -04:00
parent 6bb863da97
commit df5b0f5161
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5 changed files with 121 additions and 53 deletions
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50
R.py
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@ -17,7 +17,9 @@ from vsp import has_vsp
# ===================================================
# Defining the logic of R
"""
Defining the Logic of R
"""
x = PropositionalVariable("x")
y = PropositionalVariable("y")
@ -59,12 +61,13 @@ logic_rules = implication_rules | negation_rules | conjunction_rules | disjuncti
operations = {Negation, Conjunction, Disjunction, Implication}
R_logic = Logic(operations, logic_rules)
R_logic = Logic(operations, logic_rules, "R")
# ===============================
# Example 2-element Model of R
"""
Example 2-Element Model of R
"""
a0 = ModelValue("a0")
a1 = ModelValue("a1")
@ -103,7 +106,7 @@ designated_values = {a1}
logical_operations = {
mnegation, mimplication, mconjunction, mdisjunction
}
R_model_2 = Model(carrier_set, logical_operations, designated_values)
R_model_2 = Model(carrier_set, logical_operations, designated_values, "R2")
interpretation = {
Negation: mnegation,
@ -112,25 +115,36 @@ interpretation = {
Implication: mimplication
}
print(R_model_2)
# =================================
# Generate models of R of a given size
"""
Generate models of R of a specified size
"""
print("*" * 30)
model_size = 2
solutions = generate_model(R_logic, model_size, print_model=True)
print("Generating models of Logic", R_logic.name, "of size", model_size)
solutions = generate_model(R_logic, model_size, print_model=False)
print(f"There are {len(solutions)} satisfiable models of element length {model_size}")
print(f"Found {len(solutions)} satisfiable models")
for model, interpretation in solutions:
print(has_vsp(model, interpretation))
print("-" * 5)
print("*" * 30)
######
# Smallest model for R that has the variable sharing property
# This has 6 elements
"""
Showing the smallest model for R that has the
variable sharing property.
This model has 6 elements.
"""
a0 = ModelValue("a0")
a1 = ModelValue("a1")
@ -149,7 +163,7 @@ mnegation = ModelFunction(1, {
a2: a2,
a1: a4,
a0: a5
})
}, "¬")
mimplication = ModelFunction(2, {
(a5, a5): a5,
@ -193,7 +207,7 @@ mimplication = ModelFunction(2, {
(a0, a2): a5,
(a0, a1): a5,
(a0, a0): a5
})
}, "→")
mconjunction = ModelFunction(2, {
@ -238,7 +252,7 @@ mconjunction = ModelFunction(2, {
(a0, a2): a0,
(a0, a1): a0,
(a0, a0): a0
})
}, "∧")
mdisjunction = ModelFunction(2, {
(a5, a5): a5,
@ -282,12 +296,12 @@ mdisjunction = ModelFunction(2, {
(a0, a2): a2,
(a0, a1): a1,
(a0, a0): a0
})
}, "∨")
logical_operations = {
mnegation, mimplication, mconjunction, mdisjunction
}
R_model_6 = Model(carrier_set, logical_operations, designated_values)
R_model_6 = Model(carrier_set, logical_operations, designated_values, "R6")
interpretation = {
Negation: mnegation,
@ -297,7 +311,5 @@ interpretation = {
}
print(R_model_6)
print("Satisfiable", satisfiable(R_logic, R_model_6, interpretation))
print(f"Model {R_model_6.name} satisfies logic {R_logic.name}?", satisfiable(R_logic, R_model_6, interpretation))
print(has_vsp(R_model_6, interpretation))