Subjective Logic

Subjective Logic

by Audun Jøsang                                 Norwegian

The Inherent Subjectivity of Beliefs

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, but our perception of that reality will always remain subjective.

In a world of post-truth politics, fake news and alternative facts, we need a reasoning framework that takes into account the relative trustworthiness of information sources and the truthfulness of the information they provide. The possibility that information sources can be subjective and deceptive must be seriously considered in order to safely navigate the maelstrom of modern media. If you trust sources that are untrustworthy for giving advice about objective facts, then you'll also become untrustworthy. It's difficult to distinguish between what is trustworthy and what is not, we often push rational arguments aside and rather trust whatever gives us a comfortable feeling. A Darwinistic explanation for our difficulty to perceive objective truth is that our brain evolved for the purpose of survival, which is different from the purpose of perceiving objective reality.

We all run parallel bookkeeping of truths, meaning that we often say something other than what we really think, depending on the situation. There can be many rational reasons for this, such as e.g. politeness, to get attention and be liked, to avoid blame, to be loyal, to disinform and influence, to censor truth and oppress opposition, to deceive and swindle, or otherwise to obtain some advantage or profit for ourself or for our own community. 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 in society. 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 civilization when we hold and promote different and conflicting subjective truths. This is especially critical if one part uses force to dictate its own subjective truth onto others. Incompatible subjective truths are always an element in warfare. People will always have different subjective truths, and hence it's a fundamental challenge for humanity how this can be handled in a peaceful way.

The battle of truths during centuries and millennia have produced a variety of different and often conflicting systems of truths and beliefs held by e.g. political, ethnic and religious communities. Some communities are open to discuss the validity of their beliefs. Other communities consider their beliefs to represent the absolute truth, meaning that their beliefs have been cemented into dogma that are not up for discussion. Participation in a community often requires the adoption of its beliefs, which can also be called values, faith or ideology. The community provides support, comfort and safety, which in turn generates positive feelings. Since belonging to a community fills these basic human needs, individuals often do not question the community's beliefs. This simple principle can be expressed as: "If believing it makes me feel good, then it must be true". In this way, our compass for assessing the validity of truths is largely governed by whether it gives a positive feeling, often irrespective of whether it makes sense rationally. Many people consider their lives and community to depend on a set of truths. The thought of questioning these truths would be equivalent to questioning the foundation for their lives and community, which naturally would be painful for many.

To express different truths or to argue against beliefs held by a community can even be dangerous. Members of a community could regard any opposing views as a menace to their community's standing or existence, and hence could try to eliminate such opposing views by various means. In some communities it is common to use threats, force and violence to dictate subjective truths on others. You need a lot of courage to stand firm to your beliefs under such coercion. Many people will typically follow their instinct of survival by adopting the community's truths, and even more so by becoming agents of the same coercive methods to further propagate the same truths. In such communities truth is obviously not based on objective reason, but on power structures. This is especially the case in communities, and in some cases whole countries, where a handful of people or even just a single person have the power to dictate their own subjective truths to the whole community. Some communities even have cultural systems of beliefs that explicitly encourage members of the community to eliminate conflicting views by force and violence. Such power structures and belief sets generate more conflict, violence, destruction and suffering, and hence have no place in a civilized society.

A constructive and ethical way of discussing truths is by argumentation, which can take place between members within the same community or between members of separate communities. Everyone must be allowed to freely search and select information sources, must get unrestricted access to the information sources they want to use, and must be allowed to judge for themselves the trustworthiness of each source. The goal of argumentation is primarily to reach a consensus on truth, but that will not always be possible. Therefore, argumentation should also have as objective to reach understanding and respect for each other's different beliefs in case consensus can not be reached. The philosophy of relativism says that truth always must be considered relative to the observer. This means that separate individuals and communities perfectly well can have dogmatic beliefs about their respective incompatible truths, because they respect each other's different beliefs and understand that any truth must be seen in the context of the individual or community which expresses that truth. To repudiate relativism is not only to deny the fact that our beliefs are subjective, it is also to advocate intolerance and conflict. To acknowledge the inherent subjectivity of beliefs is to embrace the philosophy of relativism which is a basis for tolerance and peace.

Reasoning under Uncertainty with Subjective Logic

Subjective logic can be used to mathematically express and visualise the subjectivity of truths, and to formally fuse and analyse them for deeper insight and understanding. With subjective logic it is possible to mathematically analyse the relationship between different subjective truths that are held and promoted by different sources.

Subjective logic is a calculus for probabilities expressed with degrees of epistemic uncertainty where sources of evidence can have varying degrees of trustworthiness. In general, subjective logic is suitable for modeling and analysing situations where information sources are relatively unreliable and the information they provide is expressed with degrees of uncertainty. For example, it can be used for modeling subjective trust networks and subjective Bayesian networks, and for intelligence analysis.

Arguments in subjective logic are subjective opinions which can express relatively uncertain probabilities about propositions or trust in sources of propositions. Binomial opinions correspond to Beta PDFs (Probability Density Functions), whereas multinomial opinions correspond to the more general Dirichlet PDFs. This makes subjective logic suitable for reasoning with evidence represented in the formalism of traditional statistics. Subjective logic generalises Bayes' theorem, where arguments are subjective opinions, instead of just probabilities. For details and theory see the book on subjective logic, the Wikipedia page on Subjective logic, or the tutorial on subjective logic given by Lance Kaplan and Audun Jøsang at FUSION 2019 in Ottawa, July 2019.

Demonstrators of Subjective Logic

Subjective Logic

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, Book Depository,, and (US), (China), (GB), (Germany/EU), (India), or (France).

Subjective Logic

The book describes representations of subjective opinions, decision making and the various subjective logic operators. It describes the subjective Bayes' theorem which takes epistemic uncertainty into account. The book also describes relevant applications of subjective logic in the areas of computational trust networks and Bayesian networks, which together represent subjective networks.

Published Oct. 23, 2020 1:20 PM - Last modified June 10, 2022 12:37 PM