stylistic:tone, quality:corruption, linguistic:voice_change
Subjective logic

Modus tollens represents an instance of the abduction operator in subjective logic expressed as:

where ω Q A {\displaystyle \omega _{Q}^{A}} denotes the subjective opinion about Q {\displaystyle Q}, and (ω Q | P A, ω Q | ¬ P A) {\displaystyle (\omega _{Q|P}^{A},\omega _{Q|\lnot P}^{A})} denotes a pair of binomial conditional opinions, as expressed by source A {\displaystyle A}. The parameter a P {\displaystyle a_{P}} denotes the base rate (aka. the prior probability) of P {\displaystyle P}. The abduced marginal opinion on P {\displaystyle P} is denoted ω P ‖ ~ Q A {\displaystyle \omega _{P{\tilde {\|}}Q}^{A}}. The conditional opinion ω Q | P A {\displaystyle \omega _{Q|P}^{A}} generalizes the logical statement P → Q {\displaystyle P\to Q}, i.e. in addition to assigning TRUE or FALSE the source A {\displaystyle A} can assign any subjective opinion to the statement. The case where ω Q A {\displaystyle \omega _{Q}^{A}} is an absolute TRUE opinion is equivalent to source A {\displaystyle A} saying that Q {\displaystyle Q} is TRUE, and the case where ω Q A {\displaystyle \omega _{Q}^{A}} is an absolute FALSE opinion is equivalent to source A {\displaystyle A} saying that Q {\displaystyle Q} is FALSE. The abduction operator ⊚ ~ {\displaystyle {\widetilde {\circledcirc }}} of subjective logic produces an absolute FALSE abduced opinion ω P ‖ ~ Q A {\displaystyle \omega _{P{\widetilde {\|}}Q}^{A}} when the conditional opinion ω Q | P A {\displaystyle \omega _{Q|P}^{A}} is absolute TRUE and the consequent opinion ω Q A {\displaystyle \omega _{Q}^{A}} is absolute FALSE. Hence, subjective logic abduction represents a generalization of both modus tollens and of the Law of total probability combined with Bayes' theorem.