Editing Modus tollens (section)

===Subjective logic===
''Modus tollens'' represents an instance of the abduction operator in [[subjective logic]] expressed as:

<math display="block">\omega^{A}_{P\tilde{\|}Q}= (\omega^{A}_{Q|P},\omega^{A}_{Q|\lnot P})\widetilde{\circledcirc} (a_{P},\,\omega^{A}_{Q})\,,</math>

where <math>\omega^{A}_{Q}</math> denotes the subjective opinion about <math>Q</math>, and <math>(\omega^{A}_{Q|P},\omega^{A}_{Q|\lnot P})</math> denotes a pair of binomial conditional opinions, as expressed by source <math>A</math>. The parameter <math>a_{P}</math> denotes the [[base rate]] (aka. the [[prior probability]]) of <math>P</math>. The abduced marginal opinion on <math>P</math> is denoted <math>\omega^{A}_{P\tilde{\|}Q}</math>. The conditional opinion <math>\omega^{A}_{Q|P}</math> generalizes the logical statement <math>P \to Q</math>, i.e. in addition to assigning TRUE or FALSE the source <math>A</math> can assign any subjective opinion to the statement. The case where <math>\omega^{A}_{Q}</math> is an absolute TRUE opinion is equivalent to source <math>A</math> saying that <math>Q</math> is TRUE, and the case where <math>\omega^{A}_{Q}</math> is an absolute FALSE opinion is equivalent to source <math>A</math> saying that <math>Q</math> is FALSE.  The abduction operator <math>\widetilde{\circledcirc}</math> of [[subjective logic]] produces an absolute FALSE abduced opinion <math>\omega^{A}_{P\widetilde{\|}Q}</math> when the conditional opinion <math>\omega^{A}_{Q|P}</math> is absolute TRUE and the consequent opinion <math>\omega^{A}_{Q}</math> 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]].<ref>Audun Jøsang 2016:p.92</ref>