1. A fact or statement taken for granted; a supposition (a logical assumption).
2. The act of taking (esp. someone else’s debt or other obligation) for or on oneself; the agreement to so take (assumption of a debt). — assume, vb.
implied assumption. The imposition of personal liability on a land purchaser who buys subject to a mortgage and who deducts the mortgage amount from the purchase price, so that the purchaser is treated as having assumed the debt. [Cases: Mortgages 279. C.J.S. Mortgages § 395.]