# Subjective Logic Operators Demo

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Subjective logic takes opinion arguments which can be binomial, multinomial or hypernomial. A binomial opinion about a proposition is an ordered tuple (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 prior probability of the proposition in the absence of specific belief or disbelief. The default value is the relative atomicity, i.e. 0.5 for a binary state space containing the proposition and its negation.
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 reduced confidence; and opinions where b+d=0 express vacuity of confidence. The projected probability of a binomial opinion is defined as P=b+au.

Opinions can be visualized on opinion triangles as shown below. 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 'a' is shown as a pointer along the base line, and the projected probability 'P' is formed by projecting the opinion point onto the base, in parallel with the base rate 'director' line.

Try various subjective logic operators in action below. You can also try the opinion visualisation demo, and the trust network demo that uses trust discounting and cumulative fusion operators for analysing a simple trust network.

The mathematical details of each operator are described in the book on subjective logic. For a summary of the operators see the subjective logic page on Wikipedia.

The following operators are implemented in the demo below: Addition, Subtraction, Complement, Multiplication, Comultiplication, Division, Codivision, Uncertainty maximization, Trust discounting, Deduction, Subjective Bayes' theorem, Abduction, Constraint fusion, Cumulative fusion, Averaging fusion, Weighted fusion, and Unfusion.

Choose an operator using the selector at the top left in the frame below. Then 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 shown on the right-most triangle.

JavaScript design by Gaëtan Bouguier. Original design concept by Simon Pope.

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Last updated: 15 August 2017.