What is now required is to give the greatest possible development to mathematical logic, to allow to the full the importance of relations, and then to found upon this secure basis a new philosophical logic, which may hope to borrow some of the exactitude and certainty of its mathematical foundation. If this can be successfully accomplished, there is every reason to hope that the near future will be as great an epoch in pure philosophy as the immediate past has been in the principles of mathematics. Great triumphs inspire great hopes; and pure thought may achieve, within our generation, such results as will place our time, in this respect, on a level with the greatest age of Greece.
– Bertrand Russell [1917]The representation dimension (page 23) has, as its top level, reasoning in terms of individuals and relations. Reasoning in terms of relations allows for compact representations that can be built before the agent encounters particular individuals. When an agent finds out about an individual, it can make inferences about that individual. This chapter outlines how, in planning, learning and probabilistic reasoning, feature-based representations can be expanded to deal also with individuals and relations. In each of these areas, the relational representation benefits from being able to be built before the individuals are known and, therefore, before the features are known. As Russell points out in the quote above, relational reasoning brings great advantages over propositional and feature-based representations.
Planning with Individuals and Relations
A robot that can deliver parcels to people needs a model of the world before it knows which parcels exist and which people may need deliveries. It might need to be programmed before it knows the environment which it will inhabit. A tutoring system needs to work for multiple students and multiple problems, and needs to be programmed before it knows about the students and all of the problems. A purchasing agent, when it is being designed and built, will not know about all of the hotels and rooms it can book, and will not know about the people and their goals or preferences. In all of these cases, the agent's goals and its environment are described in terms of individuals and relations.
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