shall

auxiliary verb, present singular 1st person shall, 2nd shall or (Archaic) shalt, 3rd shall, present plural shall; past singular 1st person should, 2nd should or (Archaic) shouldst or should·est, 3rd should, past plural should; imperative, infinitive, and participles lacking.

1. plan to, intend to, or expect to: I shall go later.
2. will have to, is determined to, or definitely will: You shall do it. He shall do it.
3. (in laws, directives, etc.) must; is or are obliged to: The meetings of the council shall be public.
4. (used interrogatively in questions, often in invitations): Shall we go?

verb past should (takes an infinitive without to or an implied infinitive)

1. (esp with I or we as subject) used as an auxiliary to make the future tensewe shall see you tomorrow Compare will 1 (def. 1)
2. (with you, he, she, it, they, or a noun as subject)
   1. used as an auxiliary to indicate determination on the part of the speaker, as in issuing a threatyou shall pay for this!
   2. used as an auxiliary to indicate compulsion, now esp in official documentsthe Tenant shall return the keys to the Landlord
   3. used as an auxiliary to indicate certainty or inevitabilityour day shall come
3. (with any noun or pronoun as subject, esp in conditional clauses or clauses expressing doubt) used as an auxiliary to indicate nonspecific futurityI don’t think I shall ever see her again; he doubts whether he shall be in tomorrow

v.Old English sceal, Northumbrian scule “I owe/he owes, will have to, ought to, must” (infinitive sculan, past tense sceolde), a common Germanic preterite-present verb (along with can, may, will), from Proto-Germanic *skal- (cf. Old Saxon sculan, Old Frisian skil, Old Norse and Swedish skola, Middle Dutch sullen, Old High German solan, German sollen, Gothic skulan “to owe, be under obligation;” related via past tense form to Old English scyld “guilt,” German Schuld “guilt, debt;” also Old Norse Skuld, name of one of the Norns), from PIE root *skel- (2) “to be under an obligation.” Ground sense of the Germanic word probably is “I owe,” hence “I ought.” The sense shifted in Middle English from a notion of “obligation” to include “futurity.” Its past tense form has become should (q.v.). Cognates outside Germanic are Lithuanian skeleti “to be guilty,” skilti “to get into debt;” Old Prussian skallisnan “duty,” skellants “guilty.”