Update README.md

README.md

@@ -24,6 +24,90 @@ Training Details
 	•	Epochs: 15
 	•	Batch Size: 2
 
+# Example Usage
+
+For the following natural language argument:
+
+Eating a balanced diet and exercising regularly are key to maintaining good health. If you maintain good health, you'll have more energy throughout the day. John has been eating a balanced diet and exercising regularly for the past few months. Therefore, it's likely that John now has more energy throughout his day.
+
+This model was able to accurately break down the argument into its premises and conclusion, and give a complete proof in propositional logic form, citing lines and inference rules:
+
+Premise 1: If someone eats a balanced diet and exercises regularly, they will maintain good health. Premise 2: John eats a balanced diet and exercises regularly. Conclusion: Therefore, John has more energy throughout his day.
+ 
+Natural language proof: If a person eats a balanced diet and exercises regularly, they will maintain good health. We know that John eats a balanced diet and exercises regularly. Therefore, we can conclude that John maintains good health. From this, we can further deduce that John has more energy throughout his day. Thus, we can conclude that John has more energy throughout his day. 
+I will use the following mapping for the premises: 
+The letter 'a' represents the premise 'A person eats a balanced diet'.
+The letter 'b' represents the premise 'A person exercises regularly'.
+The letter 'c' represents the premise 'A person maintains good health'.
+The letter 'd' represents the premise 'A person has more energy throughout his/her day'.
+ 
+Propositional logic proof: 
+1. Original Premise: (a ∧ b) → c
+2. Original Premise: a ∧ b
+3. Derived Step: c (From 1 and 2, Modus Ponens)
+4. Original Premise: c → d
+5. Conclusion: d (From 3 and 4, Modus Ponens)
+
+
+For the same prompt, here is how Llama 3.1 8b Instruct performed:
+
+The argument can be broken down as follows:
+
+Premise 1: EBD ∧ ER → G (If you eat a balanced diet and exercise regularly, you'll maintain good health.)
+Premise 2: G → ME (If you maintain good health, you'll have more energy throughout the day.)
+Premise 3: EBD ∧ ER (John has been eating a balanced diet and exercising regularly for the past few months.)
+
+Conclusion: ∴ MEL (It's likely that John now has more energy throughout his day.)
+
+Here is the full proof in propositional logic form:
+
+1. EBD ∧ ER → G
+2. G → ME
+3. EBD ∧ ER
+4. ⊢ (EBD ∧ ER) ∧ (G → ME)
+5. ⊢ ((EBD ∧ ER) → G) ∧ (G → ME)
+6. ⊢ (EBD ∧ ER) → (G → ME)
+7. ⊢ (EBD ∧ ER) → ((EBD ∧ ER) → ME)
+8. ⊢ ((EBD ∧ ER) → ME)
+
+The final answer is ∴ MEL, or "It's likely that John now has more energy throughout his day." 
+
+And here is how Claude 3.5 Sonnet performed:
+
+Premises:
+P1: Eating a balanced diet and exercising regularly are key to maintaining good health.
+P2: If you maintain good health, you'll have more energy throughout the day.
+P3: John has been eating a balanced diet and exercising regularly for the past few months.
+Conclusion:
+C: It's likely that John now has more energy throughout his day.
+Mapping of premises to letters for propositional logic:
+A: Eating a balanced diet and exercising regularly
+B: Maintaining good health
+C: Having more energy throughout the day
+J: John has been eating a balanced diet and exercising regularly
+Natural Language Proof:
+
+Eating a balanced diet and exercising regularly are key to maintaining good health. (Premise 1)
+If you maintain good health, you'll have more energy throughout the day. (Premise 2)
+John has been eating a balanced diet and exercising regularly for the past few months. (Premise 3)
+Since John has been eating a balanced diet and exercising regularly, he is likely maintaining good health. (From 1 and 3)
+Since John is likely maintaining good health, it's likely he has more energy throughout the day. (From 2 and 4)
+Therefore, it's likely that John now has more energy throughout his day. (Conclusion)
+
+Propositional Logic Proof:
+
+A → B (Premise 1)
+B → C (Premise 2)
+J (Premise 3)
+J → A (Definition of J)
+J ∧ (J → A) (Conjunction of 3 and 4)
+A (Modus Ponens on 4 and 5)
+A ∧ (A → B) (Conjunction of 1 and 6)
+B (Modus Ponens on 1 and 7)
+B ∧ (B → C) (Conjunction of 2 and 8)
+C (Modus Ponens on 2 and 9)
+
+Therefore, C (John likely has more energy throughout his day)
 
 # Usage