  Some useful terminology: Given a ground model M for L and a name, function symbol or relation symbol X, we can think of I(X) as the interpretation or, to borrow a term from Gupta and Belnap, the signification of X.  Gupta and Belnap characterize an expression's or concept's signification in a world w as “an abstract something that carries all the information about all the expression's [or concept's] extensional relations in w.” If we want to interpret Tx as ‘x is true’, then, given a ground model M, we would like to find an appropriate signification, or an appropriate range of significations, for T. 