Jongsma, Bonne (2025) Signed Threshold Graphs and their Logic. Master's Thesis / Essay, Artificial Intelligence.
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Abstract
This thesis aims to bridge the gap in social network analysis between balance theory and diffusion models. Balance theory is based on signed graphs, where agents can have positive (friends) and negative relations (enemies) to other agents. Diffusion models study how a behavior, opinion or technology spreads through a network using a threshold: agents adopt if a threshold of adopted neighbors is reached. This results in a model that is updated in discrete timesteps. The combination of these two models results in signed threshold graphs, which depict how a behavior diffuses through a network of friends and enemies. The key idea is that enemies, unlike friends who copy each other, want to have opposing behavior. It is proven that the optimal state of behavior diffusion can be reached iff the graph is balanced. Afterwards, a dynamic extension of social network logic is developed for reasoning about these models. An axiomatisation is given that is proven to be sound and complete. The properties of non-overlapping, balance and completely connected are defined by including the difference operator.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Christoff, Z.L. and Verbrugge, L.C. |
| Degree programme: | Artificial Intelligence |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 02 Jun 2025 13:23 |
| Last Modified: | 02 Jun 2025 13:23 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/35239 |
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