A workable definition of computerized agents

A workable definition of computerized agentsBertil EkdahlPaul DavidssonDepartment of Software Engineering and Computer Science,University of Karlskrona/Ronneby, S-372 25 Ronneby, Sweden.E-mail: {bek, pdv}@ide.hk-r.seAbstractRecently, several suggestions for (multi-) agent theories have been presented. In order to develop a meaningful formal theory it is necessary also to specify a model, i.e., how to interpret the theory. This, in turn, requires a well-defined domain, otherwise it is not possible to define predicates, etc. We argue that current suggested agent theories do not have a well-defined domain and consequently there is neither a well-defined interpretation of the used symbols. In fact, the common interpretation is more of a metaphysical character. The reason behind the failure, we believe, is that the attempts are based on a diffuse idea of the internal structure of computerized agents, often described in terms of human-like “mental states” such as beliefs, desires, and intentions. This is in fact a circle reasoning since a computerized agent is not defined and consequently cannot have an internal structure.Because of the “internal structure”idea, a sound definition of agents in these terms is necessary to get a formal theory. We show that none of the most known agent definitions fulfills this requirement, and that it is very hard, perhaps impossible, to come up with such a definition. Another problem with current so called theories is that they aim to be very general, covering every aspect of agenthood. This is too optimistic since there is obvious evidence that some aspects of the human agency are not describable. In short, the task of developing a general agent theory is simply not feasible. Instead we argue that agent theories should be relativized to particular human-like situations without reference to obscure metaphysical interpretations as internal structures of agents that are yet to be defined. We suggest that the proper approach to constructing agent theories is to take suitable social theories and transform them to technical domains where the new artificial actors become (machine) agents. In fact, there already exist successful transformations of this kind, e.g., theories of market behavior into market-oriented programming.Keywords: Agent, agent theory, agent definition, agents and social science, computer and social science.1.IntroductionSoftware agents is a rapidly growing area of research interest. Despite the big efforts, there is still no agreement on what should be meant by “agent”. It seems as everything could be called an agent and according to Petrie (1996, p.24) there has also been such definition as “someone or something that acts on your behalf” which does not seem to throw light on the subject. Nwana (1996, p.208) expresses this vagueness as “we have as much chance of agreeing on a consensus definition for the word “agent”as AI researchers have of arriving at one for “artificial intelligence” itself —nil!” This state of affairs may be acceptable if we just were to write programs and call them agents. However, as many researchers claim that they study agent theory this is not an acceptable situation. In fact, it indicates that there is at least no coherent theory of the topic and that despite all the programs that have been written under the title “agent”, none has been valuable in a theory formation. Every program is a “one shot” with no relevance to a theory; it is just another program.Despite the difficulties in defining agents it seems that in the “agent community” there is a wish to stick to the term “agent”. We suppose this is due to its epistemological attraction, which, besides its instrumental meaning, suggests human capacities beyond that of mere calculation. A human agent is a “doer”who acts autonomously and behaves intelligently. The appealing is the same, we presume, as that behind AI, namely the wish to create more and more human-like systems and thereby get a grip on intentional properties. The belief that intentional properties can be formally described is widely held and seems to be supported by two unreasonable beliefs, viz.(i) intentional predicates can be introduced at will,(ii) once introduced, they are describable.While the analogy with human agents is attractive, it is also a source of misunderstandings.A human agent is not an agent per se but becomes an agent in different situations. This means that we cannot study agents in the same way as biological or physical phenomena but have to study agents in situations where agency emerges. Thus, it is not a general human agent that should be in focus but situations where agency occurs. Here we mean situations, which can be sufficiently described and for which agency seems to be a relevant property. Humanagents can in fact not be completely described, see e.g. Ekdahl (1997). However, we believe that human agent behavior in certain situations can be at least partially described. It is then in such situations it could be justified to talk about agents and agent theory in a figurative sense. As it is now standing the word “agent”is really watered down and has been “an umbrella term for a heterogeneous body of research and development. The response of some agent researchers to this lack of definition has been to invent yet some more synonyms, and it is arguable if these solve anything or just further add to the confusion.”(Nwana 1996, p.208) As examples Nwana mentions knowbots, softbots, taskbots, userbots, robots, personal agents, autonomous agents and personal assistants. This division is certainly not what we mean by the situations mentioned above since the confusion remains in each part.In this article we assert that agent situations, and not agents, should be the area of investigation. In the next section we discuss agent definitions and the relation between models and theories. Based on the conclusion that no formal definition exists, and thus no formal agent theory, we then introduce the idea of situation-specific theories, which are social theories transferred to the computer domains.2.Models of agentsThe essence of a theory is to be a description of a model. In natural sciences, theory formation starts from a model. When we have an idea (a hypothesis) about how part of reality can be regarded, we form a theory consisting of axioms that describe what we believe are true, i.e., our beliefs constitute the model. When interpreted, the description will make predictions about reality (since not every case computable from the theory is observed). Hence, the purpose of a natural science theory is to be predictive and to give us more information of how the world is organized from the point of view of our beliefs (model).Mathematical theories, on the other hand, are partly different from natural science theories because in mathematics the study of structures is of interest. Thus, in mathematics the situation is sometimes the other way around, namely “What interesting models can be the result of a certain set of axioms?”. The Euclidean geometry is such an example of where the change of the fifth axiom led to very interesting models, even useful in physics.Because of their connections to human (and animal) agency (which is part of reality), we will treat agent theories on a par with theories of natural sciences.2.1 Models and definabilitySo, if a theory is going to be established, we have to start with the model. A model has the following general form{}pmnccffRRA,...,,,...,,,...,,111=A, where, in our case, A is the set of agents, s'i R are relations (predicates) between agents, s'j f are functions and s'k c are names of elements in A. In fact, we do not believe that there are any functions between agents, nor any need to name some of the agents. However, this is unimportant since for the moment we are more interested in the set A. What are the elements of A? Is it definable? If not, then it cannot be justified to assert that there is a theory of agents since in that case there is no model.Let us call a set definable if there is some property (predicate) )(xP such that a is the unique object satisfying P, i.e.))((axxPx=⇔∀)(xP may be expressed in a natural language, for example English, together with mathematical symbols. Since there are only countable many English expressions, there are only countable many definable sets. (Astonishingly, not all ordinals are definable.) For convenience we will use the notation{})(:x Pxa=.What counts as a property? Intuitively any meaningful assertion in English about the variable x is a property. Then, does “x believes b” or “x is a cup” be a property? Obviously, we need a rigorous definition of what should count as a property. Since it is necessary to know which elements belong to A and which do not, we insist that the predicate is recursive, i.e., effectively decidable (by Church’s Thesis). However, no one has given a recursive predicate for agents so the set A is not yet recursively defined.12.2 Agent definitionsThat there exists no generally accepted definition of “agent” is not news for most “agent researchers”. It has been pointed out by Nwana (1996) and Petrie (1996) among others. (Franklin and Graesser (1996) provide a comprehensive list of proposed agent definitions.) According to Nwana the set of agents will never be defined, i.e., there is no recursive predicate that characterizes the set.1Of course, a set can be defined without being recursive. For example {}↓=)(:xxK xϕ where xϕ is the x-th partial recursive function is well defined. K is recursive enumerable (r.e.) but not recursive so K is not even r.e. but still well defined. A definition of agents comparable with K should be worthless and this is why we claim the set of agents in the model to be decidable.As mentioned above, if A is not defined then it is obviously impossible to establish a model for agents and consequently there cannot exist a theory of agents. In spite of this, many researchers argue that they study formal agent theory (Wooldridge and Jennings, 1995).However, as none of these theories are based on a well-definition set of agents, it is impossible to define any predicates (relations) for the set of agents.Let us determine in detail what is missing in current proposed agent theories, besides the set A , by taking the natural numbers as an example.The language in which we are doing arithmetic consist ofRelation symbol . ≤,Function symbols . ⋅+ , ,Numerical Constants . ... ,2,1,0Structure for this language is ...,2 ,1 ,0 , , , , ⋅+≤=ωN where ω is the natural numbers. (It is convenient to let the relation symbol and the function symbols be the same as for the corresponding relation and functions in the model.)If we are now going to establish a theory of arithmetic we have to do this in form of axioms (or axiom schemata) which show the properties for the relations and the functions in the structure. The theory R is an example of a theory for the natural numbers.R1. z y x =+, if z y x =+ R2. z y x =⋅, if z y x =⋅ R3. y x =¬, if yx ≠ R4.)0 ... 1000(0x v v v x v v =∨∨=∨=→≤∀ R5. )00(0v x x v v ≤∨≤∀It is the axiom schemata R1 – R5 that basically is the theory, not the language itself.Now let us see what could be considered as axioms in theories of the kind that many agent researchers suggest. First, there is only one predicate, believe , which,as far as we understand, has its ordinary meaning; “a believes b ” means that the agent a believes that the proposition b is true. Let us write the relation as b)Bel(a,2. If this is a relation in a structure (model) it means that the set in the structure, the domain, must be AxB where A is the set of agents and B is the set of beliefs. The set B is not related to A . So, what is a set of beliefs? How is it defined? The answer is that there is no such a set as B . Taking B as “everything that could possibly be believed” is not a good definition since it tacitly understood that there is someone who held this belief, e.g., an agent. It is also impossible to decide if an2For the sake of simplicity, we do not here make any difference between b and the Gödel number of b.element belongs to B or not without guessing or ask someone. Thus, AxB cannot be defined and hence there is no relation b)Bel(a,. There is a simpler way to recognize that there exists no such relation as b)Bel(a,.It is namely what we believe about the world that becomes our model, i.e., the model is our belief. This has been unfolded at great length in [Ekdahl, 97] and we will just give a short justification of the proposition.Copernicus held the belief that the sun and the planets orbit around the earth. This becomes his model from which he built a theory. It was when the predicted value from the theory did not agree with observations that the model was questioned and finally abandon to the benefit of another belief. The whole of physics rests on beliefs and all physical theories are theories of beliefs. In fact every empirical science rests on beliefs, which forms the models. Thus there is no such relation as belief and accordingly there is neither a theory of agents as those suggested. Second, no axioms are stated and this is peculiar because why should one claim that there is a theory of agents if no theorem can be proved from it? As we have already mentioned, the whole purpose with a theory is to prove theorems, i.e. to make predictions.Let us again examine definitions of “agent”. Nwana seems to realize the difficulties with formal descriptions and suggests three minimal demands for an agent:autonomy, learning and cooperation. However, this leads to the following characterization based on these new “predicates”:{})()()(: x Coop x Learn x Auto x A ∧∧=.Given that the predicates of the definition are recursive, this would of course be an adequate definition.Unfortunately, this means that we are facing the same problem as before, and if we do not manage to give recursive definitions of these new predicates, it seems that nothing has been gained. Franklin and Graesser (1996) has proposed the following “definition”: “An autonomous agent is a system situated within and part of an environment that senses that environment and acts on it, over time, in pursuit of its own agenda and so as to effect what it senses in the future.” Such a characterization seems to be of little value and even Petrie questions this definition and asks “But what is an operational, objective definition of autonomy?” (1996,p.25). Thus, he is asking for a recursive predicate that would make the set A (effectively) decidable. It is easy to present similar objections against definitions of learning and cooperation. So, Nwana’s attempt to define agents was not more successful than the previous attempts.The way above to characterize agents may be useful when discussing agents in informal contexts, but as a basis for a general agent theory that will not do. Russell and Norvig put it this way: "The notion of an agent is meant to be a tool for analyzing systems, not an absolute characterization that divides the world into agents and non-agents." (1995, p.33) However, as there are obvious reasons for having formal theories of agency, it would beunfortunate if we just had to give up the idea. In the next section we will sketch another approach to agent theories that do not suffer from the limitations discussed above.3.Agent situationsThe human calculating capability is the model of computation. All attempts to prove that this model is not appropriate have so far been fruitless. However, there are some researchers who believe that the Turing machine model can also capture other capabilities of man, or at least that other human capabilities could be shown to be on par with the calculating capability. All attempts to prove this has failed. Yet, this idea has led to serious attempts to ascribe social abilities to programs (agents) (e.g., Werner (1989)). The problem is exactly the same as before, namely to give a suitable definition, this time about what should be meant by “social ability”.Wooldridge & Jennings have as one of four criteria that agents should have a social ability: “agents interact with other agents (and possible humans) via some kind of agent communication language.”(1995, p.4) Similarly, in Nwana’s characterization of agents, cooperation is one of three attributes that an agent should exhibit. “In order to cooperate, agents need to possess a social ability, e.g., the ability to interact with other agents and possibly humans via some communication language”(1996, p.209). Thus, if programs send messages to each other this is regarded as a social ability. In our opinion, this is not much of a social ability and seems as a violation of the true meaning of the word. For example, UNIX-tasks “communicate” with each other and operating systems “communicate”with other programs but no one think about it as a social ability.We think it is fair to say that one characteristic of the software agent movement is the “dream” to formalize man’s social ability. One of the forerunners is von Neumann who tried to lay the foundation of a mathematical theory of biological phenomena. Together with Morgenstern (1944), he analyzed rational behavior in situations where there are conflicting goals. He did not try to describe an over-all rational agent but realized that he had to stick to situations where rationality could be defined. Also, in his book The Computer and the Brain (1958), which discusses the difference and similarities between the computer and the brain, he was well aware of the important of a precise definition of the basic concepts used. It is a regrettable fact that no significant progress has been made since von Neumann. We believe that the reason for this is probably that social abilities are at most partially describable. Nevertheless, these strivings show that there is a strong tendency to compare the behavior of interacting computer programs with human group behavior. As we have shown, what has been significant, possibly with few exceptions, is the attempt to describe the human social ability without having a model.3.1 Agent and social theoriesNow, in the spirit of von Neumann, we will turn the perspective to social situations where there are both a model and at least a rudimentary theory. Thus, instead of trying to describe the human social ability in general we look at limited social situations applicable to some technical domain. Our idea here is to take ideas from the social sciences, to which we count all sciences that study group behavior of human and animals, and apply them to technical domains. Typical areas where we find theories of this kind are, as already has been mentioned, economics, biology, and game theory.Social ConceptionFig. 3.1When we face a problem where many different programs are going to “cooperate”(or compete), we should try to find a social model, analogous to our problem and whose corresponding description is possible to transfer to computer programs. Figure 3.1 illustrates the idea. If we have a situation in a technical domain, which seems to resemble a social situation (which is described in some social theory), we adopt the model, possibly with some changes, then transfer the theory into a software system. If only an informal theory exists, we first have to formalize or adapt the social model. The benefit of this approach is that we can be sure that there is a model of the program, which, as we have seen above, is not always the case today. Given that the discrepancy between the models is fairly small, we can, of course, use the social theory to make predictions about the corresponding technical situation in the same way as the social scientist can make predictions about the corresponding social situation.Then, which social theories are transferable to technical domains? As pointed out in section 2, all predicates of the theory must be recursive (computable) in order to be describable. We discussed one example of a non-recursive predicate in detail, namely “belief”. In fact, it turns out that most, if not all, predicates corresponding to “mental states”are non-recursive. Hence, we should be very careful when trying to transfer social theories that are based on “mental states”.The social theory is a description of how human agents proceed in a certain situation and the corresponding programs become a theory of the similar behavior of a technical system. The programs, when executed, are acting in accordance with human agents. It is this correspondence that makes it reasonable to talk about computerized agents.3.2 Examples of situation-specific agenttheoriesActually, the approach we suggest is not new. In fact, it has been successfully applied in several different domains. Take for instance the idea of market-oriented programming (Clearwater, 1996) which exploits the concept of markets and uses the (economical) model of them to build computational economies to solve particular problems such as distributed resource allocation. This approach is inspired in part by economists' metaphors of market systems “computing”the activities of the (human) agents involved, but also by the “agent researchers” view of modules in a distributed system as autonomous agents. In market-oriented programming these metaphors are taken literally, and are directly used to implement the distributed computation as a market price system. The program agents interact in a very restricted manner; by offering to buy or sell quantities of commodities at fixed unit prices. When the computing system reaches equilibrium, the computational market has indeed computed the allocation of resources throughout the system, and dictates the activities and consumption of the various modules.A particularly good example from our point of view is the work of Wellman (1994). By adopting one of the most well known market models, the general equilibrium theory (Hildenbrand and Kirman, 1976), he specifically proposes to build on concepts and theory of microeconomics as a formal foundation. This work is a clear step in turning the idea of computational markets from an attractive but informal metaphor for a software system into a full-fledged theory for an artificial agent.3.3 CharacterizationIn our perspective we consider agent technology as the translation of social theories into computer programs. The idea can be more precisely formulated in the following way:(i)Every theory, informal or formal, thatdescribes situations in which two or morehumans or animals cooperate or compete iscalled a social theory.(ii)Agent theories are social theories transformed or adapted to computerprograms.(iii)The actors in the social theory become agents in the corresponding agent theory.We should remember that not all social theories are transferable to technical domains. For instance, all predicates of the social theory must be decidable. Besides, most social theories are not formalized, implying that the agent researcher first has to do this before it can be transferred to an agent theory. Moreover, it may be the case that not all social theories are interesting in the context of software agents.4. ConclusionsMany researchers in the field of software agents seem annoyed by the fact that there is no proper definition of the term “agent”. All the proposed definitions are a sure sign of this. Unfortunately, most, if not all, proposals aim at defining agents with the human agent as a starting-point. It is here that the problems start, i.e., with the assumption that all relevant aspects of human agenthood are describable. There are convincing indications that this is not the case. However, we do believe that the behavior of human agents in certain situations is describable and we argue that such situations are in fact what social theories describe.As we have argued above, agent theories should be seen as the application of social theories to computer science. Software agents should not be studied in isolation. It is necessary to have a good understanding of certain social theories in order to develop good agent theories. This implies that agent programming is in fact an interdisciplinary task.The main advantage of our approach is twofold:(a)It emphasizes the resemblance to social theoriesand brings into focus the question of whichsocial theories that can be transferred or adaptedto technical situations. (This may even be aresearch area.)(b)The engineering process and the development oftools for agent theories can be more directed.The drawback with our approach is that we cannot define agents without respect to a suitable social theory. It would be preferable if the set of agents were defined independent of other theories. The problem is that the great focusing on social abilities from a computational perspective is not justified and has so far not contributed to a suitable definition. However, we imagine that the focusing on social theories and their transferability to computer programs will make it possible to improve this situation.ReferencesClearwater, S.(ed.), Market-oriented programming: Some early lessons, World Scientific, 1996.Ekdahl, Bertil, Computerized Agents form a Linguistic Perspective, Ph.D. thesis, Lund University, Lund, Sweden, October 1997.Franklin, Stan and Graesser Art, Is It an Agent, or Just a Program?: A Taxonomy for Autonomous Agents, Proceedings of the Third International Workshop on Agent Theories, Architectures, and Languages (published as Intelligent Agents III, LNAI 1193), pp. 21-35, Springer-Verlag, 1997.Hildenbrand, W. and Kirman, A.P., Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras, North-Holland, 1976.Neumann, John von and Morgenstern, O., Theory of Games and Economic Behavior, Princeton Univ. 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