However, with the logical-consequence semantics, there are non-standard models of the program, in which, for example, add(s(s(0)), s(s(0)), s(s(s(s(s(0)))))), i.e. 2 + 2 = 5 is true. But with the satisfiability semantics, there is only one model, namely the standard model of arithmetic, in which 2 + 2 = 5 is false.
howEvER, wiTH the logiCAl-consequEnCe SemantiCs, thEre ARe non-stanDaRD models of The pRoGRAM, iN whICh, fOR EXample, aDd(s(S(0)), s(S(0)), s(s(s(s(s(0)))))), i.e. 2 + 2 = 5 Is true. but wIth the SatisFiAbiLiTy semanTIcs, there iS oNly ONe model, Namely ThE sTaNdarD model of AritHmEtIC, in whicH 2 + 2 = 5 iS falSe.