The database would consist of one table that associates arbitrary text strings with public key IDs, and another table containing cryptographically-signed affirmations or refutations of the entries in the first table.
An example of an arbitrary text string could be a legal name, an email address, "inventor of the Linxu kernel", "CEO of Acme, Inc.", etc.
Everybody is free to claim anything they want, and everyone else is free to confirm or refute it. A suitable algorithm would be used to sort out these statements based on the user's location in the web of trust to estimate the veracity of any particular statement.
The value of the web of trust depends on getting people to actually use it so the tools for managing it would need to be enjoyable to work with instead of painful. That's one reason I think making the user interface similar to a social network because the emperical evidence suggests that people like using Facebook more than they like using GPG or OpenSSL. The other reason is that social networks better model how people actually interact in real life so making the web of trust operate that way is more intuitive.
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