Jan M. Żytkow APPROXIMATE KNOWLEDGE OF MANY AGENTS AND DISCOVERY SYSTEMS 1. Introduction Automated discovery systems have been growing rapidly throughout 1980s as a joint venture of researchers in artificial intelligence (AI), and (to a lesser degree) in philosophy of science [1]; [3]. Many systems have been constructed and applied, primarily to various re-discovery tasks. The theory of heuristic search guided the work, but this theory applies to just about everything in AI, while there has been little specific theoretical foundation for automated discovery. On April 14th, 1989, Professor Rasiowa gave a lecture at George Mason University on Poset-based Logics of Approximate Reasoning. The lecture linked subjects of Epistemic Logics, Information Systems, Semi- Post Algebras, and Rough Sets. The common thread has been sets of agents, arranged in partial orders and lattices. One of the key notions has been a predicate d t p i, by which agent t approximates predicate p i. As expected, the lecture has been dominated by formal systems, their basic properties and semantics. As a former philosopher, who for many years engaged in discussions on epistemic logics, knowledge operators and approximate reasoning, I have been sceptical of their practical use in application to human mind which notoriously eludes portrayals in formal theories. It seems hard to expect human conformity to formal assumptions of a system of logic. Suddenly I realized the potential for applications in the domain of computer discovery systems, my main area of research. A long discussion on the following day brought more light on the use of logics for multi-agent systems. Unlike humans, computer systems can be inspected in every detail. They can be also altered to meet formal requirements of a given system of logic or algebra. Theory of multiple agents can enter the stage in various ways. Different versions of one system can be considered as agents, who 185
form a set partially ordered by the capabilities available in each version. Different parts of a system can be viewed as individual agents, too. This interpretation is natural in multiprocess systems. The apparatus of logic can be used externally to the computer system, for instance by the developer, to reason about properties of the system, or to improve the design. But it is also possible and more attractive to put multi-agent logics to internal use by the systems, so that agents actually reason by means of a given logic or algebra. Many further encounters with logics for approximate knowledge followed. Especially important for me has been a number of meetings with Professor Rauszer at the Warsaw Banach Center in the Fall 1991. She contributed generously her time and advice, exploring the links between rough set, multi-agent logics and automated discovery. My personal impression has been that Helena Rasiowa, Cecylia Rauszer, Andrzej Skowron, and other logicians, as well as the inventor of rough sets Zdzislaw Pawlak have been intrigued and even thrilled by the possible applications of their mathematical work in discovery systems. At present, the applications have been external, helping to organize the thinking of the developer and aiding the design of multi-agent systems. But a larger impact of their visionary work will crop up in the future internal applications. That task is more difficult, because it requires operationalization of the logic formalism. We need decision procedures and proof mechanisms whenever available. We also need a number of extensions which I discuss at the end. Builders of automated discovery systems resemble constructors of gothic cathedrals; possessed builders, whose ambition is to construct bigger and more capable structures. Surely the cathedral builders knew the laws of statics, but the theory trailed far behind practice. The builders push for theory advancements when no higher buildings can be raised. The constructors of discovery systems will soon face limitations of their artifacts and seek new theories, among those the new logic foundations. 2. Many agents in a discovery system Rasiowa, Rauszer and their collaborators (e.g., [HR75], [CR47]) focused primarily on agents who can approximate a predicate or a set. We can call 186
them measuring agents. We will focus on such agents and at the end we will briefly explore the role for theoretical agents. Empirical inquiry includes experimentation with the physical world. Here discovery systems offer measuring agents the role of empirical semantics. Measuring agents are needed to make direct links between the system working on the computer and the physical world. Automation of those links is enabled by variety of hardware (manipulators and sensors) designed for scientific laboratories and furnished with computer interfaces. Manipulators such as burets, heaters, and valves or sensors such as balances, thermometers, and ph meters are plentiful. They allow robotic systems to perform a vast range of scientific experiments. Taking advantage of new robotic hardware, in recent years we have developed a number of robotic discoverers. Some make chemistry experiments and require no moving parts ([4], 1992), while other take on the form of mobile robots and robot arms. What part of a robotic system can be treated as a measuring agent? The hardware of a particular instrument is necessary but not sufficient. Hardware must be driven by a piece of software called device driver. Individual measurements of instruments controlled by device drivers, however, are rarely sufficient as scientific data. To measure a magnitude that characterizes a true physical property of objects in an experiment setup S, the sensing must be adjusted to the specifics of S and its environment. This often requires combined use of several sensors and manipulators, guided by an operational definition, that is an algorithm that controls many elementary actions of sensors and manipulators. Only jointly they lead to justified measurements that interpret a physical property. In every experiment setup there is room for improved accuracy of actions and measurements, by construction of more adequate operational definitions. This is a discovery process. Both the setup S and operational definitions can be re-arranged with the help of empirical regularities, discovered in S for the earlier versions of operational definitions. In conclusion, a measuring agent is defined by a combination of operational definition, device drivers, and instruments. Such agents make up the necessary physical interpretation of physical properties and facts for the automated discoverer. Unlike formal semantics defined in metamathematics, this is a non-formal definition. Little can be proved about each interpretation, because no formal structure is assumed on the part of semantics. The semantics, however, can be evaluated empirically, and should satisfy the requirements of stability of readings, minimality of measurement 187
error, and generality of the scope of measurements. All these virtues are reflected in the quality of the subsequently discovered knowledge. 3. A closer look at measuring agents Why is it useful to have many agents available for a single physical magnitude? Why not use only the best agent, who may translate to an ideal in the lattice of agents? There are several reasons. Often there is no best one among available agents, as their ranges of application overlap. For instance, each balance applies only in a specific range of situations. Many agents, whose readings are less accurate, possess advantages of greater stability. This is why it is appealing to represent a set of procedures by a partially ordered set of agents or by a lattice. Since each agent comes with its own indiscernibility relation, rough logic [CR47] is a natural application. Different relations combine according to the rules of rough set theory. The ideals, even if physically unavailable, can be mathematically defined, and they make practical sense, too. They may, for instance, denote the limitations of discernibility for a given repertoire of empirical procedures and instruments. A multiprocess system makes the multi-agent perspective particularly appealing and useful, because different agents can be identified with different processes. In robotic discoverers multiprocessing is used for practical purposes. Some sensor readings must be taken in parallel, some other may take a long period of time. A single process approach may suffer inefficiency, when it must wait repeatedly for sensor readings. A specific approximation logic [HR75] or rough logic for many agents [CR47] can help in many ways, guiding our reasoning about measuring agents, helping in the design of multi-agent collaboration and in seeking a unified theory of operational procedures. But in addition, a given logic and a given partial ordering may be used in the actual reasoning by the agents. 4. New challenges Measuring agents, as represented in the current framework of rough logic, are limited in many ways. Equivalence relation, interpreted as indistinguishability, should be replaced by tolerance, which seems empirically more 188
appropriate and fundamental. Recent work that expands the notion of rough set to rough functions and operations on rough functions (Pawlak, 1995) meets many problems but can aid automation of discovery. Manipulating agents who control the empirical setup are as necessary as measuring agents. Equally needed are theoretical agents who use results of measurements and manipulations to discover regularities and to reason about them. The algebraic approach to logic, proposed in semi-post algebras and expanded by Rasiowa and Rauszer to multi-agent systems, can be a very useful guide to reasoning about knowledge by theoretical agents. Reasoning about knowledge adds new dimensions to reasoning about facts handled by today s rough logic or alternative approaches such as statistics. Acknowledgments: Helena Rasiowa, Cecylia Rauszer, Andrzej Jankowski, Zdzislaw Pawlak and Andrzej Skowron made significant contributions to the new perspective on discovery systems outlined in this paper. References [1] P. Langley, H. A. Simon, G. Bradshaw and J. M. Żytkow, Scientific Discovery: Computational Explorations of the Creative Processes. Cambridge, MA: MIT Press 1987. [2] Z. Pawlak, On Rough Derivatives, Rough Integrals, and Rough Differential Equations, ICS Research Report 41/95, Warsaw University of Technology 1995. [3] J. Shrager and P. Langley (eds.), Computational Models of Scientific Discovery and Theory Formation, San Mateo, CA: Morgan Kaufmann 1990. [4] J. M. Żytkow, J. Zhu and R. Zembowicz, Operational Definition Refinement: a Discovery Process, Proceedings of the Tenth National Conference on Artificial Intelligence, The AAAI Press, 1992, pp. 76 81. Computer Science Department Wichita State University; Wichita, KS 67260-0083 - USA & Institute of Computer Science, Polish Academy of Sciences 189