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Semantics as vaporware

Symbolic KRR systems are observer-level theories of agents' representation and reasoning capabilities, and as such should not be used as agent-level implementation vehicles, or only with extreme care. They can be used to describe, discuss, and hypothesize about agents' behavior among scientists (observers), but that is something very different from providing an actual agent with such capabilities. Analogously, we may describe the workings of a car engine using the language of differential equations, with an accompanying semantics. One would not expect, however, to find an interpreter for differential equations in an engine upon opening it up, nor does it seem likely that we could build a working engine based on such an interpreter. Why then would we want to use a KRR language to implement a working agent (or agent's mind)? Granted, a car engine and a mind are very different things, at some level of description at least.

KRR systems are attempts at formalizing the way we intuitively and consciously perceive the world to be, including the way we perceive our own mind to work, in order to endow an artificial agent with a similar understanding, and hopefully with similar capabilities to use that understanding in order to function intelligently in the world. As such it relies heavily on introspection and conscious awareness of the world and ourselves as a source of things to formalize. But in the course of studying perception on the one hand and the physical world on the other hand, we have come to realize that there is an enormous gap between the physical world as we now understand it to be and our conscious perception of that world. That gap is somehow bridged by our perceptual apparatus, and our knowledge of how that works is still spotty at best. Moreover, the perceptual apparatus is entirely ``invisible'' to the conscious mind, to such an extent that even some scientist have proposed that we just perceive the world directly, without any intervening mechanism at all (e.g., [Luce 1954]). Strange as that may seem, it is a good indication of how convincing and ``real'' conscious awareness of things is, or seems to be. In AI, it has taken the concerted efforts in the field of computer vision to enable computers to see, to realize just how hard the problem is, and how well our brains manage to deceive the conscious part of us into thinking perception is something direct and easy. Even color vision, which this dissertation deals with some aspects of, and which seems so natural and effortless to us, is a far from understood problem of amazing complexity. In the light of all this, it seems limited at best to try to endow an artificial agent with intelligence by merely trying to formalize our conscious awareness of things and ignoring the very mechanisms which lead to such an awareness in the first place.

Although other kinds of models are emerging, some (like artificial neural networks) based more closely on our present understanding of how the brain works, we may feel that their level of description and operation is too low, that they therefore offer little hope for working models of mind, and thus that any viable approach has to encompass some kind of KRR capability. Elsewhere we have argued for hybrid models of autonomous agents, comprising both KRR and other ``lower level'' mechanisms [Lammens et al. 1994][Hexmoor et al. 1993b][Hexmoor et al. 1993c][Hexmoor et al. 1992], and there are some signs that the neural network community is trying to re-incorporate results from ``traditional'' AI and KRR [Zeidenberg 1990]. If we accept the premise that using a KRR language is a valid approach to implementing (part of) an agent's mind, we should be aware of the unusual nature of trying to use an observer-level description as an agent-level implementation. One of the consequences, I believe, is that we have to treat the semantics of our descriptive language differently.

Ordinarily, it suffices that there exists a systematic interpretation (semantics), and that all observers share it (or share the preferred interpretation). We then hope that we can restrict the formal properties of the representation language in such a way that (1) we can express anything in the domain of interpretation in the formal language (representational adequacy) and (2) the interpretation of formal statements derived from others we consider to be true, by means of formal inference, does not disagree with the facts of the domain of interpretation, as we perceive them (inferential soundness). In addition, we may require that (3) anything we perceive to be true of the domain of interpretation can be derived from a set of basic premises by formal inference (inferential completeness). Semantics does not enter into the inference process; it merely serves as a tool for theorists to convince themselves and each other that the formal system does what it is supposed to do. But although semantics has been effectively shut out from the inference process, it is eventually the yardstick with which the usefulness of models is measured. We hope that in turning the crank of the formal system, it will provide us with formal conclusions representing true statements about the domain of interpretation which we had not ourselves perceived before. It is a tool for us to understand more about the domain of interpretation.

If we want a KRR system to be part of an agent-level implementation of a mind, however, things are different. It is no longer the independent theorist who will use a semantic yardstick to measure the performance of the formal system and hope to learn more about the domain of interpretation by turning the formal crank. What we are after in implementing a mind is to give the artificial agent itself the same kind of ``understanding'' of the domain of interpretation as we have, to give it the same access to that domain as we do. In other words, the semantics of the model can no longer exist independently of the system itself; it has to be part and parcel of it. In terms of the subject matter of this dissertation, we do not want to find out more about color by building a formal system and turning its crank, but rather we want an artificial agent to understand color the way we do, i.e., to perceive color the way we do. No amount of axioms and inferences in a formal system will ever give an agent that understanding if it cannot identify the referents of the terms that are supposed to be interpreted as representing colors, i.e., if it does not have an integral semantic model of color terms as part and parcel of its ``mind''. Color perception in this case provides the required grounding for a set of terms of the KRR system. It constitutes an internal, referential semantic model of color terms, as I explained above. Even if we could provide a blind agent with enough formal representations (without the associated semantics) to not produce any statements about color which we would find in disagreement with our understanding of it, it could hardly be said to understand those statements if it has no way to identify or discriminate color in its environment at all, i.e., to make color play a role in its interaction with its environment. This is, of course, what Steven Harnad has called the symbol grounding problem [Harnad 1990].

I conjecture that an ungrounded agent will never be able to adapt to its environment in an effective way, or to interact with its environment in a useful way, two things we can safely regard as prerequisites for intelligence. The reason it cannot do these things is that it is effectively cut off from its environment as long as its representations are ungrounded, i.e., as long as they are formal only. In that respect I consider the type of approach as exemplified by [Rapaport 1988] as insufficient, viz. that semantics is reducible to syntax. It seems to arise out of an exclusive preoccupation with language, and I believe one cannot deal with language without dealing with cognition in general, including perception. Language is the top of a mountain of cognition, and we cannot hope to arrive at it without climbing.

For a slightly different approach to the same problem, let's go back to the view of a KRR system as a formal language for a moment. A formal language consists of an alphabet , a syntax describing the legal strings of the language , a set of axioms that are given as true statements of the language, and a set of inference rules that allow us to derive new statements from given ones [Manin 1977]. Any statement that can be derived from using the rules in is a theorem, and the set of all derivable theorems plus the axioms is a theory. The inference rules are sound iff given a consistent set , one cannot derive a contradiction, and the formal system is complete iff all statements that are true in any model (interpretation) of the language are theorems of the language. The notion of representational adequacy described above is more difficult to formalize. Once we have defined a formal language , we have once and for all defined a corresponding theory, which we may regard as being implicit in the definition and able to be made explicit by applying the inference rules to the axioms A and any previously derived theorems. If we conceptualize the set as a space with each string represented as a point (or a vector), then the theory defined by the formal system is necessarily a subspace of that space. It is easy to see that we can change the shape and size of the theory-subspace by changing the set of axioms or the set of inference rules .

What the ungrounded symbolic approach to KRR, for instance [Rapaport 1988], is attempting to do, in my opinion, is to shape the theory-subspace such that it coincides with the space of what we as external observers would consider to be meaningful statements. It does this by introducing additional ``meaning postulates'' (axioms) or inference rules, whenever an undesirable result is produced. For example, when a natural language understanding (NLU) system happily produces sentences like ``Young old Lucy is a male girl'', additional meaning postulates are added to the underlying KRR system whose intended interpretation is that something cannot be young and old at the same time, nor male and a girl at the same time, and the inference rules used during the NL generation process are changed, if necessary, to take these constraints into account. Another example would be a meaning postulate that states that although a phrase like ``reddish green'' is syntactically well-formed, semantically it is not - or it is at least strange. One hopes, then, that introducing enough of these meaning postulates and inference rules will eventually make the theory-space converge onto the space of meaningful statements, i.e. meaningful for the human observer.

I will refer to this as the pruning problem, since it amounts to pruning down the tree of theorems of the formal system. This, I believe, is in essence what [Rapaport 1988] refers to as syntactic semantics, although he does not state it in these terms. The important thing to notice is that ``meaning'', as we humans understand it, does not enter into the picture, except as an external yardstick used by the observer to measure how well the formal system is performing. The formal system itself is blissfully unaware of any meaning. I believe that although in principle it is possible to constrain a formal system enough in this way, there is no indication that we are anywhere near that goal, or making substantial progress. Probably the largest effort in this respect is the Cyc project at MCC [Lenat 1990], the usefulness and robustness of which for practical applications remains to be shown. One of the main problems with this approach seems to be that it is not clear where such postulates should come from (whether there is a systematic ``discovery procedure'' for them), nor how many one needs, nor indeed whether their number is finite at all. The Cyc project seems to have resorted to a rather haphazard way of collecting meaning postulates (and inference rules), essentially by having team members read anything they can get their hands on and figuring out which postulates have to be added to make the system work properly [Lenat 1990].

What is the alternative? If we want to use some kind of symbolic knowledge representation formalism, we will have to make sure that it is grounded in perception and action, or embodied. Basically that means making sure that the agent using the KRR formalism is able to identify and interact with the referents of a set of distinguished terms, the directly grounded ones (cf. [Harnad 1990]). Other terms and constructs of the KR language, the indirectly grounded ones, will have to derive their meaning from this set of directly grounded terms. I will make these concepts more concrete in what follows. Indeed, this entire dissertation can be seen as a case study of the grounding of a particular set of terms: basic color terms (Section ). As sketched in Section , and explained in detail in Chapter , this approach makes a referential semantic model an integral part of the agent's machinery, rather than something that exists only on paper or in the mind of the observer. Not only can such an agent identify and interact with the referents of (a subset of) the symbols it uses, a condition I cited above for understanding, but it also provides us with a different approach to the pruning problem I mentioned before, one that looks more promising to me than the purely syntactic approach. We can prune the tree of theorems from a semantic point of view, rather than a syntactic one. That answers the question where meaning postulates come from, viz., from the constraints that are inherent in the perceptual and motor mechanisms that ground the symbols of the KR language. Embodiment really matters; one cannot study intelligence or cognition in the abstract. This approach may also provide an answer to the question how many meaning postulates are needed. I propose that they are generated on the fly, as needed, by using embodied reasoning mechanisms as well as embodied representations.

To make all of this more concrete, let's consider the grounding of basic color terms. As I will describe in section , human color perception is thought to be organized in an opponent fashion, red and green being one opponent pair, and blue and yellow another (Figure ).

That means that opponent color percepts cancel each other, so that we can well perceive yellowish green or reddish blue, but not reddish green or yellowish blue (the mutual cancelation results in an achromatic white or grey perception). If our model of color perception and color naming (i.e., our semantic model of basic color terms) uses an analog color space representation that conforms to that organization, our agent can employ an analog style ``reasoning'' process to think and speak about color, which basically amounts to mental imagery, or envisioning the referents of terms in the perceptual space they derive their meaning from.

Let's assume for the sake of simplicity that the semantics (meaning) of a basic color term (e.g. ``red'') is a function from that term to a point in the color space and that the semantics of a compound color term (e.g. ``yellowish green'') is compositional, i.e. it is a function of the meanings of its constituent terms. In particular, let's assume that the point which is the image of the compound term under the semantic function is halfway between the points that are the images of the component terms. The meaning (which I take to be just the image of the term under the semantic function) of ``yellowish green'' is then a point in the color space corresponding to the color one perceives when superimposing yellow and green lights, i.e., a yellowish green or greenish yellow color, and the same for the meaning of ``red-green''. However, in the latter case, the resulting percept is achromatic (white or gray), i.e., not a color in the common sense. Hence, there is no need for a syntactic meaning postulate specifying that there is something semantically odd about ``red-green'' as a color term but not about ``yellowish green'': it is immediately obvious from envisioning the meanings of these terms.

So, in a sense, having a semantic model as part of an agent's mind provides meaning postulates, but they do not have to be represented explicitly. How many such postulates are there? Given that the perceptual space is represented in an analog fashion, the number is infinite for all practical purposes, up to the limit of resolution of the perceptual space. The semantics of terms used in KRR is now no longer something extraneous to the KRR system, but provides essential constraints on the reasoning process. It is not yet clear to me how these constraints should affect the reasoning process, only that they do. An agent with grounded color terms will not likely attempt to paint its office walls reddish green, for instance.

lammens@cs.buffalo.edu