THE FUTURE WORLD OF AI
H.J. van den Herik
1, Maastricht/Leiden, The NetherlandsThe future world of Artificial Intelligence should be based on results achieved and milestones passed.
DEEP BLUEs victory over Kasparov is taken as a starting point. The relation between computer-chess research and computer-science-and-law research is described in notions recognizable by both sides. The question whether intuition is an important issue in the decision process of a grandmaster or a judge is discussed. We arrive at the conclusion that knowledge is essential and that the argumentation process could profit from knowledge on the opponent. Assuming complete knowledge of the opponents evaluation function one is able to follow a particular strategy, called opponent modelling, which may result in more gains than could be achieved when looking from an uninformed point of view.Thus, opponent modelling is a new technique in the future world of AI. However, some old techniques, such as classification, may be improved in such a way that they also trigger unexpected results. As a case in point we focus on the identification of paintings. At the Universiteit Maastricht, we have developed a neural-network classification program that discriminate among paintings. We present an experiment in which the program distinguishes between paintings of Van Gogh, Cézanne and Gauguin with a 95-percentage score of being correct. However, distinguishing between two famous painters is not our research aim. This is to distinguish between a famous painter and his almost-perfect imitator. Otherwise stated: can a program certify a painting as an original Van Gogh? In the future world of AI such a program may exist.
In my inaugural address, titled Kunnen Computers Rechtspreken? (Can Computers Judge a Court Case), Van den Herik (1991) stated "Yes, computers can judge court cases provided that they come under well-defined subdomains of law." In the Netherlands, this was the start of a fruitful public discussion, which forced even the most-confirmed disbeliever to search for arguments why computers in principle cannot judge court cases. The discussion turned out to be very difficult and full of emotions. In the inaugural address distinct obstacles were listed and discussed. Many of them had a technical nature and could not considered to be fundamental obstacles. A few obstacles led to discussions on difficult topics, such as intuition. Below we present an argumentation why intuition is not an impregnable obstacle. The argumentation is taken from the world of computer chess instead of the world of law since in the computer-chess domain we have more pieces of evidence.
In the Netherlands, the world of computer chess had two firm disbelievers, viz. Professor A.D. de Groot, a well-known psychologist, and Hans Böhm, an international chess master (IM). Around 1980, they did not believe that a computer program could play at World Champion level.
Their arguments can be summarized as follows.
Assumption 1
The playing strength of chess grandmasters heavily rests on intuition (intuitive knowledge).
Assumption 2
Intuition cannot be programmed.
Conclusion
Chess programs will never perform at strong grandmaster level.
The outcome of the match
DEEP BLUE versus Kasparov proved both, De Groot and Böhm, wrong. Moreover, the issue whether intuition is programmable turned out to be of marginal importance. Here two tentative conclusions are worth to be formulated: (1) intuition defined as unconscious or subconscious knowledge is partly programmable; (2) intuition is less prominent than assumed so far when deciding upon a move in the choice-of-move problem. Future research must establish which conclusion is most relevant. We conjecture that both conclusions are equally valid and that future research will show that the fruitful combination of them is precisely what happens in chess programs. For researchers of other domains, the main question reads: Is the empirical evidence as now obvious in chess transferable to their domain (e.g., to the domain of law, or to any subdomain of law, or to the domain of the identification of paintings)?Of course, it is challenging to state that a similar technological development will take place in the world of law and arts. Although I am convinced that this will be the case, I prefer to show which new uplifting ideas result from intellectual fireworks. Many lessons can be learned from
DEEP BLUE. First, and most importantly, the notion of opponent modelling, i.e., describing an opponents behaviour in rules and tuning its own strategy on this behaviour, will set new research lines in many disciplines. Second, the perfection of DEEP BLUE with respect to the tuning of parameters and the cooperation of the distinct modules might be a challenge for law researchers to abandon the production of inadequate legal knowledge-based systems, and to shift focus on developing applicable normware (Van den Herik, 1997), i.e., software concentrating on applying norms of conduct and norms of competence (cf. Van Kralingen, 1994). In this contribution we only treat opponent modelling.2 Credits of Computer-Chess Research
The human Chess World Champion has been clearly defeated. Nevertheless, the following frequently-posed question deserves some attention: Is
DEEP BLUE truly stonger than Kasparov? In the chess world there is a ranking system that gives an indication of the playing strength of a chess player. It is based on results in tournaments and matches. It is usually called the ELO-rating system, after its designer, Professor Arpad E. Elo from the University of Wisconson (Elo, 1978), the official name being FIDE-rating system (FIDE means Fédération Internationale des Echecs; the World Chess Federation). As per July 1, 1997 Kasparovs rating reads 2820 points, this is higher than ever achieved by Robert Fischer. Considering Deep Blues victory of 3½ - 2½, the program should be assigned a (human) tournament-performance rating (TPR)2 of 2875.To obtain some insight into the future world of AI, we should have some knowledge of past milestones. The main credit of computer-chess research is substantiating the idea that a machine is capable of taking better decisions than human beings in the domain of chess. Apart from this overall achievement, there are distinct contributions in the form of computer-realized ideas, implemented techniques, and proven methods which have shown to be beneficial in other domains. In the following we mention the most important ones (in italics).
In the time frame 1950-1960 many search techniques have been developed (e.g., to determine a good move ordering resulting in ideas on best-first search). The techniques were based on (appropriate) evaluation functions. In the 1960s emphasis was laid on datastructures meant for suitable knowledge representations. The 1970s showed that exhaustive enumeration was possible, i.e., knowing the best move in any configuration, by producing databases with complete information. In the 1980s the common-subtree problem was solved by the introduction of transposition tables, a technique soon adopted in other domains. Moreover, this technique was extended to search tables, which stored additional relevant knowledge so that not only common subtrees were avoided, but also the search was guided in a heuristically-desired direction. In the frame-work of search, three new techniques developed in the course of the 1980s and 1990s are worth to be mentioned: applying null moves, conspiracy numbers, and proof numbers.
Next to these lines of searching, storing knowledge and representing knowledge, we acknowledge the development of machine-learning techniques, initiated by checkers research (Samuel, 1959, 1967) and largely exploited in the domain of chess (Quinlan, 1979). Another important technique is text interpretation, of which the newest techniques originate from the research by Baird and Thompson (1990). They used the domain of different chess notations as their application area. Others combined their efforts leading to a fruitful cooperation between the world of psychology and the world of chess. In particular, we mention the contribution by De Groot (1946) on think-aloud protocols, a technique adopted and extended by Newell and Simon (1972) and nowadays widely in use in multi-faceted forms when knowledge acquisition is at stake.
A recent form of cooperation between AI researchers and psychologists is in the domain of opponent modelling. Its formalization started in computer science and especially in computer chess, but it will be soon embraced in other domains, law and computer science among them.
In the following we explain opponent modelling by referring to two cases that caused quite a strive in the Netherlands. The first case is the case Kluivert; the football player was accused by a young lady. She argued that he together with three friends has taken her home and has raped her. Both sides had involved support from a respected lawyer, Mr. G. Spong (Kluivert) and Mr. A. Moszkowicz (young lady). The lawyers are very experienced lawyers, who know the tricks of the trade very well and who apply, in some practical sense, opponent modelling already for years. The second case is the case of the Hakkelaar (the Stammerer). The case deals with an internationally-organised gang of drugs dealers and drugs transports. Here the opponent is the Public Prosecutor. The Hakkelaar was supported by a team of four lawyers, two of them being Mr. Spong and Mr. Moszkowicz.
In the Kluivert case, both lawyers made statements with the goal to confirm their own conclusions, and with the side-effect that the conclusion space of the opponent would be narrowed. In this process of argumentation they use rules, produce reasons, and support their line of reasoning with (ad hoc) arguments. The last ten years several researchers have paid attention to such a process of exchanging arguments. Witteveen (1987) has outlined structures and strategies in a broad spectrum, but most researchers, such as Loui (1987), Pollock (1991), Hage (1993), Prakken (1993), Vreeswijk (1993) and Verheij (1996) have emphasized the formal structure of the process of argumentation. They focused on how to formalise the modelling of legal argumentation and defeat.
Hence, thorough investigations have been issued on subjects such as arguments and proofs, exceptions of rules, a semantics of rules and reasoning, the weighing of arguments, and conflict resolution. The new research line as induced by practice will focus on appropriate strategies with the requirement that they are most effective in the expected process of argumentation. Nor the best rule, neither the best reason should be posed, but the most effective one.
To understand what is most effective, an image or description of the opponent should be available. Assume that in a case three types of argument play a part, viz. economic, political, and environmental arguments. Seen from an "objective" point of view the economic argument brings in the largest benefits, but it could be better to argue with the environmental argumentation, since the opponents lawyer is sensible to it (and you know that). This implies that the environmental argumentation leads to a larger benefit than the economic argumentation, i.e., a larger benefit than a "objectively maximal possible" benefit will be reached.
In the second case a new practice emerged. There was not only an argumentation between two partners (the Hakkelaar and the Public Prosecutor), but also an expectation to influence the opinion of the judge by the argumentation. Although the characteristics of opponent modelling are clearly present, in this case we introduce the notion of subject modelling since the process aims at trying to take into account the judges "evaluation function".
The latter case is complex since the Public Prosecutor unexpectedly showed a wide range of PR activities during the process. Therefore the case could be typified as opponent modelling as well as subject modelling. An intriguing question is whether the lawyers team of the Hakkelaar consciously has performed their defence according to a predefined concept of opponent modelling, or that the team has performed an almost exhaustive enumeration of all arguments they could find without worrying on the order to be followed and without recognizing that a different order of presenting arguments could lead to a totally different course of the court case, since the judges subjective models had then been casted in a different way.
In our model we consider judges as information processors and problem solvers. This closely fits in with the model of systematic problem solving of legal cases, also known under the name of "the fish by Franken and Ter Heide" (see Figure 1) (Franken, 1991).
Legenda
P1, P2: Parties in the case
IR: Intersubjective Reference framework
Men: The global opinion
J: Judge
I: Legal Instruments
Figure 1 The Fish by Franken and Ter Heide.
The parties P1 and P2 have a court case: they are opponents and have completely different views on the case in question. They have invoked judge J to obtain a legally valid judgement. J should develop a theory on the problem submitted. Hence, J should select facts and determine which legal rules out of I are applicable. Below we disregard Js role, which is important for subject modelling as well as for answering the question: can computers judge a court case? We focus on the exchange of arguments between P1 and P2. This is important for the contest between them, the question being: who wins? We shall demonstrate that if all is known on the opponent, it is sometimes possible to choose a winning strategy, while objectively no win was possible.
5 The Formulation of a Strategy
For our demonstration, we take an example from the world of simple games. TicTacToe is known to be drawn, and it might be questioned whether knowledge of ones opponent strategy could improve on this result. First, we face the task of formulating a strategy which always leads to a draw. Then we check this formulation and investigate whether we could exploit any lapsus found. Consider playing TicTacToe by the following strategic rules R, and the heuristics stated H, to be applied in the order given (cf. Van den Herik, 1988).
R1:
if completing three-in-a-row is possible, do so.
R2:
if the opponent threatens to complete three-in-a-row, prevent this if possible.
H1:
occupy the central square whenever possible.
H2:
occupy a corner square whenever possible.
H1 and H2 have been formulated as heuristics rather than rules since they directly translate the consideration governing them, viz. that the central square is most important of all, and that among the border squares, those at the corners are more important than the others. Intuitively, it seems clear that strategy S, by definition being {R1, R2, H1, H2}, should achieve a draw, since it correctly evaluates the importance of the squares and acts on this evaluation. Yet, a program aware of the opponents strategy S may win.
Allow the program the first move as X, the sequence of moves exhibited in Figure 2 causes player X to win, where at move 2, 4 and 6 player 0 follows S.
Figure 2 Anticipating a known strategy.
The win by X is due to Xs awareness of the opponents strategy S, admittedly non-optimal, or to rephrase this statement, due to Xs successful prediction of 0s moves. X may be truthfully stated to apply opponent-modelling search in the simplest of examples.
Assume that party P
1 has two distinct arguments in position A of Figure 3. These arguments may lead to the position B and C, respectively. Next assume that party P2 in B has two arguments at its disposal: one leading to position D, the other one to position E. Moreover, in position C, party P2 has also two distinct arguments which lead to positions F and G, respectively. Finally, assume that judge Js "evaluation function" evaluates the positions as follows: D = 8, E = 7, F = 8 and G = 6 (the higher, the more favourable for P1; in game theoretic notions: P1 maximizes, P2 minimizes).Figure 3 P1 and P2 in an objective minimax procedure.
Partly P
1 would like to search for the value 8 (which is kept in D and F). However, P1 will not succeed, since in B is P1 to move and P2 will play the argument to E (with value 7), and in position C P2 will direct the search process to G (with value 6). Assuming P2 to be intelligent, it will choose position B and hence arrive at a gain of 7.Of course, P
1 and P2 do not know in advance what judge Js evaluation will be in the position D, E, F, and G, but they have their own evaluation function which simulates (or approximates) judge Js evaluation function. Assuming that P1s evaluation function coincides with Js evaluation function, would P1 then pose the argument leading to B? It seems logical, but it is not. P1s behaviour is completely dependent of (his/her knowledge of) the opponents evaluation function.Assume that P
2 provides the following evaluation:D = 7 E = 6 F = 8 G = 10
This leads to the evaluation pattern of Figure 4.
Figure 4 P1 and P2 with their different evaluations.
We observe that P
2 estimates the positions D and E as better (= lower in value) than P1; P1 and P2 have equal evaluation values in F; and in G, P2 is rather pessimistic. This pessimism of P2 can be exploited by P1 (this is the essence of opponent modelling). If P1 moves to C then P2 will not let P1 go to G, but to F, since in F the minimum of 8 and 10 resides. For P1 this means a gain of 8 instead of 7. Clearly, when going to position C, P1 took some risk since P2 could reconsider its thought processes (i.e., its evaluation function) and as yet go to G instead of F. The result then would be a gain of 6 instead of 7 for P1.The example given in Figure 4 suggests that applying opponent modelling (always) involves some risks. That need not to be the case. If P
1 is sure of P2s answer in position C (namely F) then there is no risk, but how sure is sure? Indeed, this is a question. In the TicTacToe example everything is certain, since the program being non-dynamical, is fixed. In addition to the opponents model (i.e., knowing his evaluation function) one should know the opponents behaviour. If the opponent has a reconsidering nature and the possibility exists that the opponent deviates from an earlier-computed evaluation then there is a risk. Does this mean that opponent modelling under these circumstances always involves taking a risk? No, again that need not be so. For instance, when the unbiased best argument (thus according to Js value) coincides with the opponent model, P1 can sit and wait whether P2 errs in a later stage. Theoretically, many complex conditions can be derived providing conditions when and where the risk is reduced to zero. For these, we refer to Iida et al. (1994).In practice lawyers will not wait until the opponent makes a mistake, but they will be inclined to increase the chances in gain taking a limited risk. Several strategies have been developed for practitioners who are willing to take such a risk. Returning to Figure 4, we know that P
1 can have a guaranteed gain of 7 by moving to B. By moving to C, P1 expects an additional gain of 1 (8 instead of 7), taking the "risk" of 1 (gaining 6 instead of 7). In general, the search trees will be much more complicated than shown in Figure 4. In such trees, we may decide first to maximize the gain (e.g., attempting to achieve 100 instead of 7) and consequently, if more than one branch led to 100, we may minimize a potential loss. Conservative lawyers first may minimize the potential loss (e.g., 0 instead of 1; note that this is the minimax path) and only then maximize the gains. Furthermore, it is possible to follow a balanced strategy, which falls outside the scope of this contribution (for details, cf. Iida et al. (1993, 1994)). The balanced model is a mathematical model with weighing functions.In the Kluivert case many scenarios can be set up for the process of argumentation. The current computer power some call it brute force enables us to investigate these scenarios completely. Analogously to search trees in the game of chess, we here deal with trees containing legal arguments made by the alternate parties. To achieve the results desired, three requirements should be imposed:
1 law and case law must be easily accessible for the program
(case-based access is preferred);
2 for the case under investigation the facts and the context must be adequately
represented; and
3 the opponents way of reasoning must be known (preferably in all details,
but at least partly).
When considering Spongs position, he faced the charge by the young lady and lawyer Moszkowiczs first step in the argumentation process, viz. to undo the results of the inspection of the young ladys undies as a fact to the case (note that the inspection results were not obtained according to the legally prescribed rules). For Spong the question is which scenario should he choose.
a Should he refute the matter of undies?
(Legally it is rather simple, since inspectation is time dependent; but that was also known to Moszkowicz and still he made an argument out of it )
b Should he deny that his client was involved in the case as described?
c Should he argue that the charge was not valid since it had not happened against
the young ladys will?
For all items (a), (b) and (c) it would be profitable for Spong to know what would be Moszkowiczs next step in the argumentation process. It would be even better if Spong had had an answer to all possible replies by Moszkowicz. Even more better would be if he could predict Moszkowiczs second replies through a "modelled" Moszkowicz. The network of variants may seem complex, but for an intelligent brute-force machine it is relatively easy to analyse such a network. The fundamental challenge resides in modelling the opponent. For this task information and knowledge on the opponent is essential.
10 Consequences and Conclusions on the Current State
All researchers familiar with information technology and knowledge engineering know that any piece of information on the opponent may be relevant. This is exactly why criminal organizations have such a great interest for floppies in possession of people working at the Prosecution Council. Modelling the Public Prosecutor is of the highest essence for a successful defence.
Although opponent modelling is still in its infancy, even for games such as chess and Shogi (cf. Iida et al., 1994) the research is challenging and promising. We may have high expectations of these developments.
Placing opponent modelling in the mainstream research we will opt for a position within agent technology. We believe that the time now is ripe to re-investigate the earlier ideas on subject modelling with a stress on the psychological view of the context, such as described by Schank and Abelson (1977). As a consequence we concur with Franken (1991) when he argues that the fish of Figure 1 should be adopted according to the context from which the judge operates. Under the assumption of subject modelling the figure will be enlarged by a new dimension.
In the future world of AI we do not only deal with new techniques, but also with improvements of old techniques, especially when the improvement leads to unexpected results (cf. Postma et al., 1997a, b). Determining the authenticity of artwork is difficult; so far it requires human expertise. However, human subjectivity in the authentication process may give rise to controversy. A recent example is the ongoing debate on the authenticity of Van Goghs Sunflowers. Nowadays, art experts challenge the authenticity of the Sunflowers in the possession of the Japanese insurance company Yasuda as a genuine Van Gogh, although it was generally accepted as an original Van Gogh for several decades. The lack of well-established criteria for determining the authenticity of paintings provides a challenging image-recognition task.
Paintings can be characterised in many ways and along many dimensions, such as global composition, distribution of colour and texture. In our experiments we apply a neural network to transform the feature-space representation into a representation space that is in agreement with the authentication task.
The data set
The data set used in the experiments consisted of 112 digital reproductions of paintings taken from the WebMuseum (Pioch, 1996). The 24-bit true-colour images varied in size with an approximate average of 1000 « 1000 pixels. Each pixel is defined as an rgb triplet, r, g, b
ë{0,1,...255} (rgb stands for red, green, and blue). The data set contained 49 works by Van Gogh, 49 works by Cézanne, and 14 works by Gauguin. Three instances (one of each maker) in the order stated above are shown in Figure 5. The data set was split up into two parts, one part was assigned to a training set (42+42+10) and the other part to a test set (7+7+4). The paintings were randomly distributed over both subsets.Figure 5
Examples of paintings included in the data set.Learning the authentication task
A multilayer neural network is capable of mapping points from an input space towards an output space (see, e.g., Bishop, 1995). The length of the input vector determines the dimensionality of the input space. The dimensionality of the output space depends on the number of categories needed for the classification task. In our binary classification task, three output nodes suffice, each active output represents a painter. The transformation from input to output space is achieved by an intermediate representation formed in a so-called hidden layer. The dimensionality of the representation space, d
hidden, (i.e., the number of nodes in the hidden layer) is a parameter of the network structure.The results of the experiments for the four series (G
spatial, Gchromatic, Gcombined, Gspatio-chromatic) are summarised in Table 1 for four dimensionalities (dhidden) of the representation space.TABLE 1
Generalisation performance on the authentication task.dhidden | Gspatial | Gchromatic | Gcombined | Gspatio-chromatic |
0 | 0.39 | 0.54 | 0.55 | 0.60 |
2 | 0.51 | 0.83 | 0.86 | 0.94 |
4 | 0.61 | 0.86 | 0.87 | 0.95 |
8 | 0.53 | 0.85 | 0.86 | 0.94 |
The results show poor generalisation performance without an intermediate representation (d
hidden=0). Moreover, the results with spatial features only are inferior to those of chromatic features only. Obviously, the best performances are obtained in the series where chromatic and spatial features are combined, i.e., Gcombined and Gspatio-chromatic. Evidently, the local binding of chromatic and spatial features (Gspatio-chromatic) leads to better results than their independent combination (Gcombined).Since Van Gogh, Cézanne, and Gaugain have produced their paintings roughly in the same period and hence under the same circumstances, we conclude that the spatio-chromatic representation provides an effective pre-processing stage for discriminating among painters. Two future steps are of interest. First, to raise the score of 95% up to 100%. Second, to aim at discriminating a genuine Van Gogh from a imitation. This may be a hard task and once succeeded, I am sure that there will be many disbelievers, especially since so much money is at stake.
The author expresses his gratitude towards his fellow researchers Hiroyuki Iida, Jos Uiterwijk and the late Bob Herschberg for their cooperation in the development of the notion opponent modelling (cf. Iida et al., 1993, 1994). Moreover, he thanks Eric Postma for his collaboration in the Rijksmuseum project.
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