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Symbol grounding: A non-Tarskian semantics

Tarskian Semantics has nothing to say about how descriptions of objects in plans relate to the objects in the world [McDermott 1991][p. 13].

Let's digress for a moment to some esoteric matters of semantics and reference. One problem an agent has to solve is how to find and maintain a correspondence between a referent in the world and a symbol in an agent's world model. As noted above, the referent in the world is (by necessity) only indirectly considered via its embodied Perceptuo-Motor level representation, hence the problem becomes one of aligning the Knowledge level representations with the Perceptuo-Motor level representations. From the perspective of cognitive science, the problem has been labeled the symbol grounding problem [Harnad 1990]. The question is how to make the semantics of a robot's systematically interpretable Knowledge level symbols cohere equally systematically with the robot's interactions with the world, such that the symbols refer to the world on their own, rather than merely because of an external interpretation we place on them. This requires that the robot be able to discriminate, identify, and manipulate the objects, events, and states of affairs that its symbols refer to [Harnad 1992]. Grounding is accomplished in our architecture in part through the alignment of the Knowledge and Perceptuo-Motor levels. Elementary symbols at the Knowledge level are grounded in the sense that they only attach to ``the right kind'' of representations at the Perceptuo-Motor level. If we think of the Perceptuo-Motor level as implementing categorial perception (and perhaps ``categorial action''), then the elementary symbols of the Knowledge level are the names attached to the categories. In other words, the alignment of the Knowledge and Perceptuo-Motor level constitutes an internal referential semantic model of elementary symbols. Note that, like McDermott, we do not take the Tarskian stance which requires the referents of symbols to be in the world; rather, they are system-internal, similar to what Hausser proposes [Hausser 1989], or what Harnad calls iconic representations: ``proximal sensory projections of distal objects, events, and states of affairs in the world'' [Harnad 1990]. The Knowledge level is the only level that is accessible for conscious reasoning, and also the only level that is accessible for inter-agent communication. Access to the Perceptuo-Motor level and the Sensori-Actuator level would not be useful for communication, as the representations and processing at these levels are too agent-centered and too agent-specific to be informative to other agents.

Since the Perceptuo-Motor level representations serving as the grounding for symbols of the Knowledge level are embodied (section ), equivalent symbols may have somewhat different semantics for different agents having different bodies. We don't see that as a problem, as long as the differences are not too large. Indeed, we believe that this is quite realistic in human terms as well; no two persons are likely to have exactly the same semantics for their concepts, which nevertheless does not prevent them from understanding each other, grosso modo at least (cf. [Rapaport 1988]). The problems of translation and communication in general consist at least in part of establishing a correspondence between concepts (and symbols) used by the participants. It is helpful to be able to use referents in the external world as landmarks in the semantic landscape, but one consequence of embodied semantics is that even if it is possible to establish these common external referents for symbols, there is still no guarantee that the symbols will actually mean exactly the same thing, because in effect the same referent in the world is not the same thing to different agents. If we accept this view, it is clear that approaches to semantics based on traditional logical model theory are doomed to fail, because they presuppose ``identity of referents'' and an unambiguous mapping from symbols to referents, the same one for all agents. Another problem is of course the presupposition that all objects are uniquely identifiable. The use of deictic representations does not impose such a condition; as far as our agents are concerned, if it looks and feels the same, it is the same. Nothing hinges on whether or not the objects in the agent's surroundings are really extensionally the same as the identical-looking ones that were there a moment ago or will be there a moment later.

lammens@cs.buffalo.edu