Editing Modus ponens (section)

===Subjective logic===
''Modus ponens'' represents an instance of the binomial deduction operator in [[subjective logic]] expressed as:

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

where <math>\omega^{A}_{P}</math> denotes the subjective opinion about <math>P</math> as expressed by source <math>A</math>, and the conditional opinion <math>\omega^{A}_{Q|P}</math> generalizes the logical implication <math>P \to Q</math>. The deduced marginal opinion about <math>Q</math> is denoted by <math>\omega^{A}_{Q\|P}</math>. The case where <math>\omega^{A}_{P}</math> is an absolute TRUE opinion about <math>P</math> is equivalent to source <math>A</math> saying that <math>P</math> is TRUE, and the case where <math>\omega^{A}_{P}</math> is an absolute FALSE opinion about <math>P</math> is equivalent to source <math>A</math> saying that <math>P</math> is FALSE.  The deduction operator <math>\circledcirc</math> of [[subjective logic]] produces an absolute TRUE deduced opinion <math>\omega^{A}_{Q\|P}</math> when the conditional opinion <math>\omega^{A}_{Q|P}</math> is absolute TRUE and the antecedent opinion <math>\omega^{A}_{P}</math> is absolute TRUE. Hence, subjective logic deduction represents a generalization of both ''modus ponens'' and the [[Law of total probability]].<ref>Audun Jøsang 2016:92</ref>