A logic breaking the Carnapian mold, that is thorough and fully developed, can be found in Zalta 1988. In this a class of abstract objects is postulated, some among them being ordinary. A distinction is made between an object exemplifying a property and encoding it. For instance, an abstract object might perfectly well encode the property of being a round square, but could not exemplify it. A general comprehension principle is assumed, in the form that conditions determine abstract individuals that encode (not exemplify) the condition. Identity is taken to hold between objects if they are both abstract and encode the same properties, or they are both ordinary and exemplify the same properties. In effect, this deals with problems of substitutivity. The formal theory (more properly, theories) is quite general and includes both logical necessity and temporal operators. It is assumed that encoding is not contingent, though exemplifying may be, and thus properties have both an exemplification extension that can vary across worlds, and an encoding extension that is rigid. With all this machinery available, a detailed treatment of proper names can be developed, along with much else.