Subjective logic

Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and source trust into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and relatively unreliable sources. For example, it can be used for modeling and analysing trust networks and Bayesian networks.

Arguments in subjective logic are subjective opinions about state variables which can take values from a domain (aka state space), where a state value can be thought of as a proposition which can be true or false. 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. Opinions are also related to the belief representation in Dempster–Shafer belief theory.

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 uncertainty, and can explicitly indicate the source of belief whenever required. An opinion is usually denoted as ${\displaystyle \omega _{X}^{A}}$ where ${\displaystyle A\,\!}$ is the source of the opinion, and ${\displaystyle X\,\!}$ is the state variable to which the opinion applies. The variable ${\displaystyle X\,\!}$ can take values from a domain (also called state space) e.g. denoted as ${\displaystyle \mathbb {X} }$. The values of a domain are assumed to be exhaustive and mutually disjoint, and sources are assumed to have a common semantic interpretation of a domain. The source and variable are attributes of an opinion. Indication of the source can be omitted whenever irrelevant.

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