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Subjective logic : ウィキペディア英語版 | Subjective logic Subjective logic is a type of probabilistic logic that explicitly takes uncertainty and belief ownership into account. In general, subjective logic is suitable for modeling and analysing situations involving uncertainty and incomplete knowledge.〔A. Jøsang. Artificial Reasoning with Subjective Logic. ''Proceedings of the Second Australian Workshop on Commonsense Reasoning'', Perth 1997. (PDF )〕〔A. Jøsang. A Logic for Uncertain Probabilities. ''International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems.'' 9(3), pp. 279–311, June 2001. (PDF )〕 For example, it can be used for modeling trust networks and for analysing Bayesian networks. Arguments in subjective logic are subjective opinions about propositions. A binomial opinion applies to a single proposition, and can be represented as a beta distribution. A multinomial opinion applies to a collection of propositions, and can be represented as a Dirichlet distribution. Through the correspondence between opinions and Beta/Dirichlet distributions, subjective logic provides an algebra for these functions. Opinions are also related to the belief functions of 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. Irrationality can be described in terms of what is known as the fuzzjective. ==Subjective opinions== Subjective opinions express subjective beliefs about the truth of propositions with degrees of uncertainty, and can indicate subjective belief ownership whenever required. An opinion is usually denoted as where is the subject, also called the belief owner, and is the proposition to which the opinion applies. An alternative notation is . The proposition is assumed to belong to a frame of discernment (also called state space) e.g. denoted as , but the frame is usually not included in the opinion notation. The propositions of a frame are normally assumed to be exhaustive and mutually disjoint, and subjects are assumed to have a common semantic interpretation of propositions. The subject, the proposition and its frame are attributes of an opinion. Indication of subjective belief ownership is normally omitted whenever irrelevant.
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