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and the validity of modus ponens cannot be taken for granted.

Probability calculus

If and , then must lie in the interval . For the special case , must equal .

Subjective logic

Modus ponens represents an instance of the binomial deduction operator in subjective logic expressed as:

where denotes the subjective opinion about as expressed by source , and the conditional opinion generalizes the logical implication . The deduced marginal opinion about is denoted

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