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Erschienen in:
Mechanizing Bisimulation Theorems for Relation-Changing Logics in Coq Kapitel lesen Erstes Kapitel lesen

2020 | OriginalPaper | Buchkapitel

A Logical Analysis of the Interplay Between Social Influence and Friendship Selection

verfasst von : Sonja Smets, Fernando R. Velázquez-Quesada

Erschienen in: Dynamic Logic. New Trends and Applications

Verlag: Springer International Publishing

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Abstract

This paper is part of a series of proposals for using logic to analyse social networks. It studies the intertwining of two forms of information dynamics: social influence, through which an agent’s behaviour, opinions or features are affected by those of her social connections, and friendship selection, through which an agent chooses her social connections based on their common behaviour, opinions or features. The text provides a logical analysis of the two forms of dynamics (the main ingredients in the phenomenon known as homophily) as well as of their interaction, discussing also some of their variations.

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Vorheriges Kapitel A Dynamic Epistemic Logic Analysis of the Equality Negation Task
Nächstes Kapitel A Four-Valued Hybrid Logic with Non-dual Modal Operators
Fußnoten
1
For an overview on the topic we refer to [16] (see also [17, 18]), where the authors discuss the main developments in the literature and indicate that homophily exists on a wide array of sociodemographic and behavioral and value-based dimensions.
 
2
It will be useful to consider the ‘dual’ function https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/MediaObjects/480838_1_En_5_Figa_HTML.gif , returning the set of positions https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/MediaObjects/480838_1_En_5_Figb_HTML.gif each agent \(\mathtt {i}\in \varvec{\mathcal {A}}\) holds on topic \(T \in \varvec{\mathcal {T}}\), and defined as https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/MediaObjects/480838_1_En_5_Figc_HTML.gif .
 
3
Definition 4.3 presents an alternative in which an agent’s new stance on topic T depends on the stances of all the agents to which she is socially connected, regardless of whether it is on topic T or on another.
 
4
For contrast, [11] proposes an operation through which two agents become socially connected if and only if they are similar enough and some agent can act as the middleman. See Definition 4.4 for an alternative that restricts the pool of candidates for friendship.
 
5
The labels of the diagrams are as in Item (i) through the whole Example.
 
6
Consider a one-topic case with positions \(\{ p,q \}\) and agents \(\{ \mathtt {a}, \mathtt {b}, \mathtt {c} \}\), their initial positions being https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/MediaObjects/480838_1_En_5_Figu_HTML.gif and the initial network being just reflexive edges. The repetition of(i) social influence with \(\tau \,{=}\,1\) (no effect), (ii) friendship selection with https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/480838_1_En_5_IEq178_HTML.gif (adding only symmetric edges between \(\mathtt {b}\) and both \(\mathtt {a}\) and \(\mathtt {c}\)), (iii) social influence now with https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-38808-9_5/480838_1_En_5_IEq182_HTML.gif (no effect) and (iv) friendship selection now with \(\theta \,{=}\,1\) (removing the just added edges) does not stabilise.
 
7
For contrast, a parallel composition, affecting both agents and social networks at once, would require a new modality.
 
8
In modal languages cases, one could work directly with a semantic characterisation of the language’s expressivity, i.e., with some form of bisimulation [27, Section 2.2].
 
9
Again, although not shown, the labels of the diagrams are as in Item (ii) through the whole Example.
 
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Metadaten
Titel
A Logical Analysis of the Interplay Between Social Influence and Friendship Selection
verfasst von
Sonja Smets
Fernando R. Velázquez-Quesada
Copyright-Jahr
2020
Buch
Dynamic Logic. New Trends and Applications

Print ISBN: 978-3-030-38807-2

Electronic ISBN: 978-3-030-38808-9

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-38808-9_5

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