An Etymological Dictionary of the German Language/Annotated/sollen
sollen, verb, ‘to owe, be in duty bond, be said to,’ from Middle High German soln (scholn), Old High German solan (scolan), preterite present, ‘to owe, be obliged, be allowed, become, be indebted, be fitting.’ The corresponding abstract Schuld, feminine, ‘debt, guilt,’ proves, like Gothic skulan, ‘to be indebted, be bond to pay,’ that skal, ‘to owe,’ is the root (the loss of the guttural, by which the 1st person skal became sol in Old High German and Middle High German, is surprising). From this root a preterite present common to Teutonic was formed, which assumed the function of an auxiliary verb; compare English shall and Dutch zal. For further details see grammars.