Subjective Logic

Subjective Logic

by Audun Jøsang

Belief Reasoning with Subjective Logic

Subjective logic is a calculus for subjective opinions which in turn represent probabilities affected by degrees of uncertainty. It can for example be used for modeling subjective trust networks, for modelling subjective Bayesian networks, for inteligence analysis and for subjective logical argumentation. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty, incomplete knowledge and different world views. It generalises Bayes' theorem by making it applicable to subjective opinions.

A subjective opinion can express trust in a source or it can express belief about events/propositions. Binomial opinions correspond to to Beta probability density functions, and multinomial opinions correspond to the more general Dirichlet probability density functions. This makes subjective logic suitable for reasoning with evidence represented as Beta or Dirichlet probability density functions. For details and theory see the the book on subjective logic or the Wikipedia subjective logic page.

Subjective Logic Demonstrations

Book on Subjective Logic

Subjective Logic: A Formalism for Reasoning Under Uncertainty, 1st edition 2016. The book is available from multiple online stores inlcuding Springer and Amazon.com (US), Amazon.cn (China), Amazon.co.uk (GB), Amazon.de (Germany/EU), or Amazon.in (India).

This book describes the subjective opinion representation, decision making with subjective opinions and the various subjective logic operators. The book also describes relevant applications of subjective logic in the areas of computational trust networks and Bayesian networks, which when combined represent subjective networks.

In a world of fake news and alternative facts, subjective logic gives each individual the necessary tools for reasoning about the relative trustworthiness of information sources and the reliability of the information they provide. The possibility that information sources can be subjective and deceptive must be seriously considered in order to safely navigate and find order in the chaos of online media.

When trying to correctly perceive the reality around you, be aware that the truth you see is mostly subjective, and that objective truth is elusive. We can assume that an objective reality exists, as "das Ding an sich" (the-thing-in-itself) in the pholisophy of Kant, but our perception of that reality will always be subjective. Subjective logic provides a framework for analysing the relationship between different subjective truths that are held and promoted by different, or sometimes even the same sources.

We all run parallel bookkeeping of truths, meaning that we often say something else than what we really think. There can be many rational reasons for this, such as politeness, fear of sanctioning, or otherwise to obtain some advantage. In addition, it's not always black and white, as we often don't know clearly whether we pretend to believe or we genuinely believe something. Whatever the case, our tendency to promote our own subjective truth as objective is driven by our instinct to thrive and survive. To promote subjective truth might help us as individuals or groups to locally prosper and reach our goals. However, in the long term it's detrimental to the stability of global civilisation when we hold and promote different and conflicting subjective truths.

Subjective Logic

Tutorial on subjective logic given at FUSION 2016 in Heidelberg, July 2016.

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Last Updated 1 February 2017