For complete KnowledgeTree operation in Salesforce, users will need read access to the following fields in the corresponding objects.

Account Contact Lead  Case Opportunity
Id Email Company  CaseNumber
Industry FirstName  Email  Id CreatedDate
LastViewedDate Id FirstName  LastModifiedDate CloseDate
Name LastName Id  LastViewedDate Id
NumberOfEmployees Name Industry  Origin Name
Website OwnerId LastName  Priority OwnerId 
LastModifiedDate Phone Name  Reason StageName
  LastModifiedDate Title  Status LastModifiedByID 
  LastViewedDate Phone  Subject LastModifiedDate
    Status  Type LastViewedDate
    LastModifiedDate   Probability

Product2 OpportunityLineItems
Id Id

Additionally,  if fields are restricted for specific profiles, you will not be able to use rules for those restricted fields.