E.A. Feigenbaum and J. Feldman (Eds.). Computers and Thought. McGraw-Hill, 1963. This collection includes twenty classic papers by such pioneers as A. M. Turing and Marvin Minsky who were behind the pivotal advances in artificially simulating human thought processes with computers. All Parts are available as downloadable pdf files; most individual chapters are also available separately. COMPUTING MACHINERY AND INTELLIGENCE. A. M. Turing. CHESS-PLAYING PROGRAMS AND THE PROBLEM OF COMPLEXITY. Allen Newell, J.C. Shaw and H.A. Simon. SOME STUDIES IN MACHINE LEARNING USING THE GAME OF CHECKERS. A. L. Samuel. EMPIRICAL EXPLORATIONS WITH THE LOGIC THEORY MACHINE: A CASE STUDY IN HEURISTICS. Allen Newell J.C. Shaw and H.A. Simon. REALIZATION OF A GEOMETRY-THEOREM PROVING MACHINE. H. Gelernter. EMPIRICAL EXPLORATIONS OF THE GEOMETRY-THEOREM PROVING MACHINE. H. Gelernter, J.R. Hansen, and D. W. Loveland. SUMMARY OF A HEURISTIC LINE BALANCING PROCEDURE. Fred M. Tonge. A HEURISTIC PROGRAM THAT SOLVES SYMBOLIC INTEGRATION PROBLEMS IN FRESHMAN CALCULUS. James R. Slagle. BASEBALL: AN AUTOMATIC QUESTION ANSWERER. Green, Bert F. Jr., Alice K. Wolf, Carol Chomsky, and Kenneth Laughery. INFERENTIAL MEMORY AS THE BASIS OF MACHINES WHICH UNDERSTAND NATURAL LANGUAGE. Robert K. Lindsay. PATTERN RECOGNITION BY MACHINE. Oliver G. Selfridge and Ulric Neisser. A PATTERN-RECOGNITION PROGRAM THAT GENERATES, EVALUATES, AND ADJUSTS ITS OWN OPERATORS. Leonard Uhr and Charles Vossler. GPS, A PROGRAM THAT SIMULATES HUMAN THOUGHT. Allen Newell and H.A. Simon. THE SIMULATION OF VERBAL LEARNING BEHAVIOR. Edward A. Feigenbaum. PROGRAMMING A MODEL OF HUMAN CONCEPT FORMULATION. Earl B. Hunt and Carl I. Hovland. SIMULATION OF BEHAVIOR IN THE BINARY CHOICE EXPERIMENT Julian Feldman. A MODEL OF THE TRUST INVESTMENT PROCESS. Geoffrey P. E. Clarkson. A COMPUTER MODEL OF ELEMENTARY SOCIAL BEHAVIOR. John T. Gullahorn and Jeanne E. Gullahorn. TOWARD INTELLIGENT MACHINES. Paul Armer. STEPS TOWARD ARTIFICIAL INTELLIGENCE. Marvin Minsky. A SELECTED DESCRIPTOR-INDEXED BIBLIOGRAPHY TO THE LITERATURE ON ARTIFICIAL INTELLIGENCE. Marvin Minsky.
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing, beforehand, the possible ways to solve a problem. Hence the need for an automated theorem prover that provide proofs as they would be written by a student. To achieve this objective, logic programming is a natural tool due to the similarity of its reasoning with a mathematical proof by inference. In this paper, we present the core ideas we used to implement such a prover, from its encoding in Prolog to the generation of the complete set of proofs. However, when dealing with educational aspects, there are many challenges to overcome. We also present the main issues we encountered, as well as the chosen solutions. The QED-Tutrix software [15, 19] provides an environment where a highschool student can solve geometry proof problems. One of its key features is that it allows the student to provide proof elements in any order, not limiting them to forward-or backward-chaining. For instance, when solving the simple problem "prove that a quadrilateral with three right angles is a rectangle", the student can provide any element of any possible proof, such as a direct consequence of the hypotheses ("if two lines are perpendicular to a third, they are parallel"), a necessary premise for the conclusion ("a rectangle is a quadrilateral that has four right angles"), or anything in between ("the quadrilateral ABCD is a parallelogram"). A second key feature is the tutoring aspect. When the student is stuck is the resolution, the software is able to provide them with relevant messages. In the previous example, if the student entered "the quadrilateral ABCD is a parallelogram" and is stuck afterwards, the software identifies that they are working on a proof using parallelogram properties, and will provide them messages such as "what is the definition of a parallelogram?" or "is there a relation between parallelogram and rectangle?" These features, the flexibility in exploration and the tutoring, are very interesting from a mathematics education perspective, but come with a cost.
When two representations are informationally equivalent, their computational efficiency depends on the information-processing operators that act on them. Two sets of operators may differ in their capabilities for recognizing patterns, in the inferences they can carry out directly, and in their control strategies (in par- ticular, the control of search). Cognitive Science 11, 65-99
We describe a prototype of a new experimental GeoGebra command and tool Discover that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary planar geometry. The paper focuses on the mathematical background of the implementation, as well as methods to avoid combinatorial explosion when storing the interesting properties of a geometric figure.