Subjective Logic Operators Demo

Subjective Logic takes opinion arguments which can be binomial or multinomial. A binomial opinion about a proposition is an ordered quadruple (b,d,u,a) where:

b: belief	is the belief that the proposition is true.
d: disbelief	is the belief that the proposition is false.
u: uncertainty	is belief that is neither committed to truth nor falsehood of the proposition.
a: base rate	is the a priori probability of the proposition in the absence of specific belief. The default value is the relative atomicity, i.e. 0.5 for a binary state space containing the proposition and its complement.

The belief, disbelief and uncertainty components satisfy b+d+u=1 Opinions where b+d=1 are traditional probabilities, opinions where 0<(b+d)<1 express degrees of ignorance, and opinions where b+d=0 express total ignorance. The probability expectation value of an opinion is defined as E=b+au. See draft subjective logic book or subjective logic on Wikipedia for more details. See also various opinion visualisation methods, and the trust network demo that uses the fusion and trust transitivity operators for analysing trust networks.

Opinions can be visualized on opinion triangles. A blue point represents a (b,d,u) triple. The b,d,u-axes run from one side to the opposite vertex indicated by the letters b, d and u. For example, a strong positive opinion is represented by a point towards the bottom right b-vertex. The base rate, also called relative atomicity, is shown as a pointer along the base line, and the probability expectation, E, is formed by projecting the opinion onto the base, parallel to the base rate `projector' line.

Scroll down to try subjective logic operators in action. Right-click on the operator symbol to select one of the operators Complement(NOT), Addition, Subtraction, Multiplication(AND), Comultiplication(OR), Division(UN-AND), Codivision(UN-OR), Discount(trust transitivity), Consensus(Fusion), Conditional Deduction or Conditional Abduction. Left-click and drag the opinion points and the base rate pointers on the left triangles to set the argument opinions. The computed result opinion is represented on the right-most triangle.

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Applet design by Simon Pope, Shane Hird and Matthew Davey.

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Last updated: 24 March 2011.