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I want to model the Middle High German sentence "Ih néhabo niêht in geméitun sô uuîlo geuuêinot" that can be glossed as "I Neg-have not-at-all in vain so much cried" meaning "I have not at all cried that much in vain". The first negation marker, the affix on the auxiliary, expresses sentential negation, the second one "niêht" is an adverbial, adjungated to the vP, strengthening the negation, similar to the "at all" part in "not at all". Now I'm wondering how this can be expressed by using lambda calculus. There's a nice theory by Regine Eckardt (2003) for the same problem in Old French but it only works for negation strengtheners that developed out of minimizers ("pas" meaning "step" etc) and not for the ones that developed out of negative indefinites like Old High German "niouuiht" meaning as much as "nothing". Any ideas?

  • The λ-calculus is just a notation, there are no logical connectives in it. That said, (higher-order) formal logic can be formulated in λ-calculus using Church’s type theory so in this sense the answer is yes. – Atamiri May 19 at 7:03

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