In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and relatively unreliable sources.
A binomial opinion applies to a binary state variable, and can be represented as a Beta PDF (Probability Density Function).
A multinomial opinion applies to a state variable of multiple possible values, and can be represented as a Dirichlet PDF (Probability Density Function).
Through the correspondence between opinions and Beta/Dirichlet distributions, subjective logic provides an algebra for these functions.
A fundamental aspect of the human condition is that nobody can ever determine with absolute certainty whether a proposition about the world is true or false.
In addition, whenever the truth of a proposition is expressed, it is always done by an individual, and it can never be considered to represent a general and objective belief.
These philosophical ideas are directly reflected in the mathematical formalism of subjective logic.
Subjective opinions express subjective beliefs about the truth of state values/propositions with degrees of epistemic uncertainty, and can explicitly indicate the source of belief whenever required.
can take values from a domain (also called state space) e.g. denoted as
The b,d,u-axes run from one edge to the opposite vertex indicated by the Belief, Disbelief or Uncertainty label.
For example, a strong positive opinion is represented by a point towards the bottom right Belief vertex.
The numerical values and verbal qualitative descriptions of each opinion are also shown.
is the non-informative prior weight, also called a unit of evidence,[4] normally set to
is the prior (base rate) probability distribution over the possible state values of
Trinomial opinions can be simply visualised as points inside a tetrahedron, but opinions with dimensions larger than trinomial do not lend themselves to simple visualisation.
is the non-informative prior weight, also called a unit of evidence,[4] normally set to the number of classes.
Transitive source combination can be denoted in a compact or expanded form.
In case the argument opinions are equivalent to Boolean TRUE or FALSE, the result of any subjective logic operator is always equal to that of the corresponding propositional/binary logic operator.
Similarly, when the argument opinions are equivalent to traditional probabilities, the result of any subjective logic operator is always equal to that of the corresponding probability operator (when it exists).
In case the argument opinions contain degrees of uncertainty, the operators involving multiplication and division (including deduction, abduction and Bayes' theorem) will produce derived opinions that always have correct projected probability but possibly with approximate variance when seen as Beta/Dirichlet PDFs.
[1] All other operators produce opinions where the projected probabilities and the variance are always analytically correct.
Subjective logic allows very efficient computation of mathematically complex models.
In such cases, subjective logic always approximates the result as an opinion that is equivalent to a Beta PDF.
Subjective logic is applicable when the situation to be analysed is characterised by considerable epistemic uncertainty due to incomplete knowledge.
The advantage is that uncertainty is preserved throughout the analysis and is made explicit in the results so that it is possible to distinguish between certain and uncertain conclusions.
Subjective trust networks can be modelled with a combination of the transitivity and fusion operators.
Evidence-based subjective logic (EBSL)[4] describes an alternative trust-network computation, where the transitivity of opinions (discounting) is handled by applying weights to the evidence underlying the opinions.
in order to apply the deduction operator and derive the marginal opinion
Traditional Bayesian network typically do not take into account the reliability of the sources.
In subjective networks, the trust in sources is explicitly taken into account.