Initial commit

R.py

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