Helpful page: https://www.mediawiki.org/wiki/Help:CirrusSearch/Logical_operators#Lucene,_MUST,_and_SHOULD

After we build it, something like this should be possible:
“citizenship=germany AND field of work=chemistry OR physics AND occupation=scientist” ->
haswbstatement:P27=Q183 haswbstatement:P101=Q2329|P101=Q413 haswbstatement:P106=Q901

Change #1248513 had a related patch set uploaded (by Jakob; author: Jakob):

[mediawiki/extensions/Wikibase@master] GQL: Support OR operator in searchItems

https://gerrit.wikimedia.org/r/1248513

Change #1248513 merged by jenkins-bot:

[mediawiki/extensions/Wikibase@master] GQL: Support OR operator in searchItems

https://gerrit.wikimedia.org/r/1248513

@Silvan_WMDE qq - how does it work now? still have to use AND and just use a pipe operator between the values? or is there an example handy somewhere?

No pipes needed. With this task we introduced or: as a second operator, that can be used within AND clauses.

This query searches for Swiss singers on beta, returning two results

query {
  searchItems(
    query: {
      and: [
        { property: "P694", value: "Q557298" } # singer
        { property: "P748", value: "Q548170" } # Switzerland
      ]
    }
  ) { edges { node { id label(languageCode: "en") } } }
}

Now the new or: operator allows searching for Swiss singers OR actors, giving three results

query {
  searchItems(
    query: {
      and: [
        { or: [
            { property: "P694", value: "Q557298" } # singer
            { property: "P694", value: "Q508927" } # actor
        ] }
        { property: "P748", value: "Q548170" } # Switzerland
      ]
    }
  ) { edges { node { id label(languageCode: "en") } } }
}

You can use or: on the top level (instead of and:) or within an AND clause as shown here. Note that it doesn't work the other way around: and: cannot be used within OR clauses. This means, that only two query levels are possible and complex nesting is effectively impossible.

Maybe we should document the query syntax in the task description

works perfectly! we should probably document this in the GraphQL doc on Wikidata as well but there's a ticket we can pick up next time https://phabricator.wikimedia.org/T419562