To facilitate discussion, I would like to describe a hypothetical color reader machine inspired by Hausser [Hausser, 1989]. This machine has a camera and a speaker. It can look at objects and tell what color they are. In that sense, it satisfies the basic premise of understanding given above.
Note that, there are at least five different levels of ``red'' in this picture:
(1) The red object out there in the real world.
(2) The image of the red object that falls on the camera.
(3) The concept red, that matches this image and presumably all other red things.
(4) The representation of the linguistic structure corresponding to the sentence ``This is red''.
(5) The symbol tokens out there in the real world ``This'', ``is'', and ``red'' carried by the sound wave.
The logical tradition concerns itself with the relationship between symbols (5) and objects (1) in the real world [Lakoff, 1987,Johnson, 1987]. One starts by linking symbols to objects, sets of objects, and tuples of objects. Other symbols are reserved to represent properties, relations and quantifiers. Syntactic rules are specified for constructing well formed formulae (wff). Assertions express propositions about the real world using wff's. Rules for algorithmic manipulation of these wff's for inference are determined [Davis, 1990]. There are two critical properties in such a system: that the inferences made by following the rules of symbol manipulation correspond to the external reality, and that things that are true in the real world can be inferred by symbol manipulation. These correspond to soundness and completeness respectively.
Note that nothing in this description include anything at the interpreter side of the picture. There is no mention of the camera, the intermediate concept, the linguistic system or the robot. In fact, it looks almost like the rules of a game. You and me sit down at a table with a game board. I throw some pebbles on the board and say, ``This pebble corresponds to the bird, that pebble corresponds to flying, etc.'' Then I tell you the rules by which I am allowed to rearrange the pebbles, and how groups of pebbles correspond to propositions, and how the rearrangements map to valid rules of inference. If you just accept my mapping and the validity of my rules, then I should be able to convince you of anything that I can come up with using my pebbles. There is no need to worry about questions like ``What is the real meaning of this pebble?'', I just told you it corresponds to the bird.
This is exactly how Cyc is built. Symbols are selected to correspond to ``things'' in the universe. A language is specified at the epistemological level to express assertions about these ``things''. Rules of inference are defined, and implemented efficiently at the heuristic level. The symbols in Cyc have no meaning attached to them. Lenat frequently makes the point that all of them could be replaced by gensyms. This means the only property by which we can distinguish the meaning of two symbols is their position relative to all the other symbols in a complicated web.