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 method 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 seemingly 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. More specifically, if my welfare increases by believing and acting according to something that is objectively false, in contrast to believing and acting according to objective truth, then my brain will solidify the belief in what is objectively false. Said simply, when my brain determines subjective truth, it doesn't matter what is objectively true, what really matters is my welfare. When I have found the subjective truth that maximizes my welfare, then that becomes my truth, and I will look no further for the objective truth. Similarly, if I have found the objective truth, but it feels uncomfortable or it reduces my welfare, then I get an urge to replace it by seeking alternative truths until I find a subjective truth that feels comfortable and that increases my welfare.

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 can be detrimental to the stability of global civilization when we hold and promote different and conflicting subjective truths. This is especially critical if one party 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 be founded 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 beliefs 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. In a discourse about truth, the party furthest away from truth us the one that stops arguing peacefully, and instead starts to use threats and violence.

A constructive and ethical way of defining truths is by discourse based on e.g. observation, analysis, documentation, reasoning, debate and argumentation. Discourse can take place among members within the same community or between members of separate communities. Threats or coercion must never be used as part of discourse. Everyone must be allowed to freely search and select information sources, must get unrestricted access to the information sources they want to use, must be allowed to judge for themselves the trustworthiness of each source, and must be allowed to freely express their own opinions.

The goal of discourse is primarily to reach consensus about truth, which is achieved relatively easily in domains like natural sciences, where consensus can be formed with direct observations and commonly accepted analytical methods, but less so in e.g. social sciences, history, economy, psychology and politics where direct observations can be difficult to make and verify. We normally expect news reporting to be based on direct observations, and thereby to represent approximate consensus. However, when different news sources report conflicting facts related to the same event, or report fictitious events, we know that some of them report fake news, e.g. for the purpose of propaganda. When you're unable to make direct observations yourself, which is normally the case, you must judge for yourself the reliability of the sources you receive the news from. For matters that can not be observed, e.g. in spiritual and religious matters, consensus can only define conventional truth, because it does not correspond to any physical reality. Note that consensus is not necessarily the goal in all situations. For example, when appreciating art, fashion and cuisine it is widely accepted, often encouraged, and seldom problematic, that people have different opinions.

Failure to reach consensus about truth within and between communities can be tragic when it leads to oppression, violence, suffering and wars. This must be avoided. Discourse about truths should therefore also have as objective to reach understanding and respect for each other's different beliefs in case consensus about truth can not be reached. The philosophy of relativism acknowledges 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 Audun Jøsang at FUSION 2022 in Linköping, July 2022.

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, Bookshop.org, and Amazon.com (US), Amazon.cn (China), Amazon.co.uk (GB), Amazon.de (Germany/EU), Amazon.in (India), or Amazon.fr (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 Feb. 14, 2024 7:52 PM