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2016 | Buch

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Subjective Logic

A Formalism for Reasoning Under Uncertainty

verfasst von: Audun Jøsang

Verlag: Springer International Publishing

Buchreihe : Artificial Intelligence: Foundations, Theory, and Algorithms

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This is the first comprehensive treatment of subjective logic and all its operations. The author developed the approach, and in this book he first explains subjective opinions, opinion representation, and decision-making under vagueness and uncertainty, and he then offers a full definition of subjective logic, harmonising the key notations and formalisms, concluding with chapters on trust networks and subjective Bayesian networks, which when combined form general subjective networks. The author shows how real-world situations can be realistically modelled with regard to how situations are perceived, with conclusions that more correctly reflect the ignorance and uncertainties that result from partially uncertain input arguments.

The book will help researchers and practitioners to advance, improve and apply subjective logic to build powerful artificial reasoning models and tools for solving real-world problems. A good grounding in discrete mathematics is a prerequisite.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

We can assume that an objective reality exists but our perception of it will always be subjective. This idea is articulated by the concept of “das Ding an sich” (the thingin-itself) in the philosophy of Kant [64]. The duality between the assumed objectiveworld and the perceived subjective world is also reflected by the various logic and probabilistic reasoning formalisms in use.

Audun Jøsang

Chapter 2. Elements of Subjective Opinions

Abstract

This chapter defines fundamental elements in the formalism of subjective logic. It also introduces a terminology which is consistently used throughout this book.

Audun Jøsang

Chapter 3. Opinion Representations

Abstract

Subjective opinions express beliefs about the truth of propositions under degrees of uncertainty, and can indicate ownership of an opinion whenever required. This chapter presents the various representations and notations for subjective opinions.

Audun Jøsang

Chapter 4. Decision Making Under Vagueness and Uncertainty

Abstract

Decision making is the process of identifying and choosing between alternative options based on beliefs about the different options and their associated utility gains or losses. The decision maker can be the analyst of the situation, or can act on advice produced by an analyst. In the following, we do not distinguish between the decision maker and the analyst, and use the term ‘analyst’ to cover both.

Audun Jøsang

Chapter 5. Principles of Subjective Logic

Abstract

This chapter compares subjective logic with other relevant reasoning frameworks, and gives an overview of the general principles of subjective logic.

Audun Jøsang

Chapter 6. Addition, Subtraction and Complement

Abstract

This chapter describes addition, subtraction and complement of subjective opinions, as a generalisation of the corresponding operators for probabilities.

Audun Jøsang

Chapter 7. Binomial Multiplication and Division

Abstract

This chapter describes the binomial SL operators ‘multiplication’ and ‘comultiplication’ [51] that correspond to binary logic AND and OR, as well as their inverse operators ‘division’ and ‘codivision’ that correspond to binary logic UN-AND and UN-OR. The operators described here assume independent argument opinions. Conditional multiplication of dependent opinions is described in Section 11.2.

Audun Jøsang

Chapter 8. Multinomial Multiplication and Division

Abstract

This chapter describes multiplication and division involving multinomial opinions, which generalise multiplication and division of binomial opinions described in the previous chapter.

Audun Jøsang

Chapter 9. Conditional Reasoning and Subjective Deduction

Abstract

This chapter first discusses conditional reasoning in general including Bayes’ theorem and then describes the deduction operator in subjective logic. The subjective Bayes’ theorem and the subjective abduction operator are described in Chapter 10.

Audun Jøsang

Chapter 10. Subjective Abduction

Abstract

This chapter describes how subjective logic can be used for reasoning in the opposite direction to that of the conditionals, which typically involves the subjective version of Bayes’ theorem.

Audun Jøsang

Chapter 11. Joint and Marginal Opinions

Abstract

Joint opinions apply to product variables e.g. denoted XY. Given a joint opinion over XY there are separate marginal opinions on X as well as on Y.

Audun Jøsang

Chapter 12. Belief Fusion

Abstract

Belief fusion is a central concept in subjective logic. It allows evidence and opinions from different source agents about the same domain of interest to be merged, in order to provide an opinion about the domain representing the combination of the different source agents.

Audun Jøsang

Chapter 13. Unfusion and Fission of Subjective Opinions

Abstract

Given belief fusion as a principle for merging evidence about a domain of interest, it is natural to think of its opposite. However, it is not immediately clear what the opposite of belief fusion might be.

Audun Jøsang

Chapter 14. Computational Trust

Abstract

Subjective logic was originally developed for the purpose of reasoning about trust in information security, such as when analysing trust structures of a PKI (Public-Key Infrastructure) [41]. Subjective logic and its application to this type of computational trust was first proposed in 1997 [40]. The idea of computational trust was originally proposed by Marsh in 1994 [71]. A survey on trust modelling is provided in [12].

Audun Jøsang

Chapter 15. Subjective Trust Networks

Abstract

A subjective trust network (STN) represents trust and belief relationships from agents, via other agents and sensors to target entities/variables, where each trust and belief relationship is expressed as a subjective opinion. The trust network is typically represented as a graph. Simple STNs have already been described in Chapter 14 on computational trust, including computation of transitive trust paths, and the computation of simple trust fusion networks.

Audun Jøsang

Chapter 16. Bayesian Reputation Systems

Abstract

Reputation systems are used to collect and analyse feedback about the performance and quality of products, services and service entities, which we simply call service objects. The received feedback can be used to derive reputation scores, which in turn can be published to potential future users. The feedback can also be used internally by the service provider, in order to improve the quality of service objects.

Audun Jøsang

Chapter 17. Subjective Networks

Abstract

This chapter provides an introduction to the concept of subjective networks (SN) as graph-based structures of agents and variables combined with conditional opinions and trust opinions [60]. SNs generalise Bayesian network modelling and analysis in two ways: 1) by applying subjective logic instead of probabilistic reasoning, and 2) by integrating subjective trust networks (STNs) which allows different agents to have different opinions about the same variables.

Audun Jøsang

Backmatter

Titel: Subjective Logic
verfasst von: Audun Jøsang
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-42337-1
Print ISBN: 978-3-319-42335-7
DOI: https://doi.org/10.1007/978-3-319-42337-1