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How to Develop a Security Controls Oriented Reference Architecture for Cloud, IoT and SDN/NFV Platforms Read chapter Read first chapter

2018 | OriginalPaper | Chapter

From Knowledge to Trust: A Logical Framework for Pre-trust Computations

Authors : Mirko Tagliaferri, Alessandro Aldini

Published in: Trust Management XII

Publisher: Springer International Publishing

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Abstract

Computational trust is the digital counterpart of the human notion of trust as applied in social systems. Its main purpose is to improve the reliability of interactions in online communities and of knowledge transfer in information management systems. Trust models are typically composed of two parts: a trust computing part and a trust manipulation part. The former serves the purpose of gathering relevant information and then use it to compute initial trust values; the latter takes the initial trust values as granted and manipulates them for specific purposes, like, e.g., aggregation and propagation of trust, which are at the base of a notion of reputation. While trust manipulation is widely studied, very little attention is paid to the trust computing part. In this paper, we propose a formal language with which we can reason about knowledge, trust and their interaction. Specifically, in this setting it is possible to put into direct dependence possessed knowledge with values estimating trust, distrust, and uncertainty, which can then be used to feed any trust manipulation component of computational trust models.

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Footnotes
1
See [2, 3, 5, 14‐16, 20] for surveys on computational trust models.
 
2
It is important to note that, even though we employ the word ‘knowledge’, we do not commit to any specific epistemological notion of knowledge. In fact, our term might refer to very different conceptions of knowledge and, in some cases, also to beliefs. Although important from a philosophical point of view, this fact does not influence the formal framework we are presenting in the paper.
 
3
Uncertainty plays a crucial role in the formalization of trust. There are many ways this concept has been described formally (see e.g. [6] for a survey). Dealing with trust in a formal way can thus help also understand how uncertainty can be modelled, providing useful insight also for fields other than computer science, e.g. economics.
 
4
It is important to stress that \( \upmu_{(i,c,\varphi )} \) is not a single function, but a family of functions. Therefore, each member of \( \upmu_{(i,c,\varphi )} \) assigns a value to the relevant atomic propositions according to the specific formula on which the function depends.
 
5
With standard conditions we refer to conditions such as the principle of non-contradiction, for which a proposition and its negation can’t both hold in the same state. An example of a non-standard condition is the fact that one proposition always implies a second one, therefore proscribing states in which the former holds while the latter doesn’t.
 
6
This is an extremely important point, since it avoids infinite regresses in the procedure and, consequently, in the evaluation process of trust formulas. If we allow arbitrary formulas in the qualitative relevance set, then an infinite regress might happen, for example, if the trust formula we are evaluating \( ( {\upomega_{i} ({\upvarphi }) \ge b}) \) appears in the qualitative relevance set of the formula for which we are trying to determine trust \( ({\upvarphi }) \). In such case, when we apply the recursive procedure and try to determine the valuation of \( \upomega_{i} ({\upvarphi }) \ge b \), the same formula will appear again in the qualitative relevance set of \( {\upvarphi } \), ab infinitum.
 
7
This condition is similar in spirit to the one we impose on the qualitative relevance set. See note 3 for further explanations.
 
8
Note that in our language a tautology is the neutral element for conjunction and the destructive element for disjunction, while a contradiction is the neutral element for disjunction and the destructive element for conjunction.
 
9
For this example, we are assuming that the R relations are equivalence relations; however, we omit the couples generated by the reflexive, symmetric and transitive closure of the relations specified in the example. The reader should consider them present.
 
10
Strictly speaking she also knows the conjunction of the two facts, but we won’t consider it, since the conjunction of the two propositions corresponding to our fact would be eliminated during the simplification of the CNF.
 
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Metadata
Title
From Knowledge to Trust: A Logical Framework for Pre-trust Computations
Authors
Mirko Tagliaferri
Alessandro Aldini
Copyright Year
2018
Book
Trust Management XII

Print ISBN: 978-3-319-95275-8

Electronic ISBN: 978-3-319-95276-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-95276-5_8

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