Subjective Logic - Subjective Logic Operators

Subjective Logic Operators

Most operators in the table below are generalisations of binary logic and probability operators. For example addition is simply a generalisation of addition of probabilities. Most operators are only meaningful for combining binomial opinions, but some also apply to multinomial opinions. Most operators are binary, but complement is unary, deduction is ternary and abduction is quaternary. See the referenced papers for mathematical details of each operator.

Apart from the computations on the opinion values themselves, subjective logic operators also take into account the attributes, i.e. the subjects, the propositions, as well as the frames containing the propositions. In general, the attributes of the derived opinion are functions of the argument attributes, following the principle illustrated below. For example, the derived proposition is typically obtained using the propositional logic operator corresponding to the subjective logic operator.

The functions for deriving attributes depend on the operator. Some operators, such as cumulative and averaging fusion, only affect the subject attribute, not the proposition which then is equal to that of the arguments. Fusion for example assumes that two separate argument subjects are fused into one. Other operators, such as multiplication, only affect the proposition and its frame, not the subject which then is equal to that of the arguments. Multiplication for example assumes that the derived proposition is the conjunction of the argument propositions, and that the derived frame is composed as the Cartesian product of the two argument frames. The transitivity operator is the only operator where both the subject and the proposition attributes are affected, more specifically by making the derived subject equal to the subject of the first argument opinion, and the derived proposition and frame equal to the proposition and frame of the second argument opinion.

It is impractical to explicitly express complex subject combinations and propositional logic expressions as attributes of derived opinions. Instead, the trust origin subject and a compact substitute propositional logic term can be used.

Subject combinations can be expressed in a compact or expanded form. For example, the transitive trust path from via to can be expressed as in compact form, or as in expanded form. The expanded form is the most general, and corresponds directly with the way subjective logic expressions are formed with operators.