Consider following two rules R1 and R2 in logical reasoning in Artificial…
2017
Consider following two rules R1 and R2 in logical reasoning in Artificial Intelligence (AI):
\(\text{R1}:\) From
\(\alpha \supset \beta \; \frac{\text{and}\; \alpha}{\text{Inter} \; \beta }\) is known as Modulus Tollens (MT)
\(\text{R2}:\) From
\(\alpha \supset \beta\frac{\text{and}\; \neg \beta }{\text{Inter}\; \neg \alpha}\) is known as Modus Ponens(MP)
Answer: D. Neither R1 nor R2 is correct. — Answer: Neither rule is correct as stated. R1 presents: From α → β and α, infer β. R2 presents: From α → β and ¬β, infer ¬α. Explanation: The first form (from…
- A.
Only R1 is correct.
- B.
Only R2 is correct.
- C.
Both R1 and R2 are correct.
- D.
Neither R1 nor R2 is correct.
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Correct answer: D
Answer: Neither rule is correct as stated.
R1 presents: From α → β and α, infer β.
R2 presents: From α → β and ¬β, infer ¬α.
Explanation:
The first form (from α → β and α, infer β) is the valid inference called Modus Ponens.
The second form (from α → β and ¬β, infer ¬α) is the valid inference called Modus Tollens.
Because each rule in the question uses the correct inference pattern but assigns the wrong name, both statements are incorrect as written; therefore the correct conclusion is that neither rule is correct.
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