A fully automatic problem solver with human-style output

This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians. The program is part of a more general project, which we also discuss.

[1]  Alfred North Whitehead,et al.  Principia Mathematica to *56 , 1910 .

[2]  G. Pólya,et al.  How to Solve It. A New Aspect of Mathematical Method. , 1945 .

[3]  G. Pólya,et al.  Mathematics and Plausible Reasoning , 1956 .

[4]  Allen Newell,et al.  The logic theory machine-A complex information processing system , 1956, IRE Trans. Inf. Theory.

[5]  Allen Newell,et al.  Report on a general problem-solving program , 1959, IFIP Congress.

[6]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[7]  W. W. Bledsoe,et al.  Splitting and Reduction Heuristics in Automatic Theorem Proving , 1971, Artif. Intell..

[8]  Robert S. Boyer,et al.  Computer Proofs of Limit Theorems , 1971, IJCAI.

[9]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[10]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[11]  Alan Bundy Analysing Mathematical Proofs (Or Reading Between the Lines) , 1975, IJCAI.

[12]  Raymond Reiter,et al.  A Semantically Guided Deductive System for Automatic Theorem Proving , 1973, IEEE Transactions on Computers.

[13]  W. W. Bledsoe,et al.  Non-Resolution Theorem Proving , 1977, Artif. Intell..

[14]  W. W. Bledsoe,et al.  Set Variables , 1977, IJCAI.

[15]  W. W. Bledsoe,et al.  Automatic Proofs of Theorems in Analysis Using Nonstandard Techniques , 1977, JACM.

[16]  G. Pólya,et al.  Mathematics and Plausible Reasoning: Vol. I: Induction and Analogy in Mathematics , 1979 .

[17]  Michael J. C. Gordon,et al.  Edinburgh LCF: A mechanised logic of computation , 1979 .

[18]  Alan Bundy,et al.  The Computer Modelling of Mathematical Reasoning , 1983 .

[19]  J. Sweller,et al.  Development of expertise in mathematical problem solving. , 1983 .

[20]  W. W. Bledsoe,et al.  Using Examples to Generate Instantiations of Set Variables , 1983, IJCAI.

[21]  J. Sweller,et al.  What do students learn while solving mathematics problems , 1985 .

[22]  Alan Bundy Discovery and Reasoning in Mathematics , 1985, IJCAI.

[23]  Dale A. Miller,et al.  Proof Explanation and Revision , 1987 .

[24]  Woody Bledsoe,et al.  A Survey of Automated Deduction11This is an enlarged version of a survey talk given by Woody Bledsoe at the Sixth National Conference on Artificial Intelligence, Seattle, Washington, July 16, 1987. , 1988 .

[25]  Alan Bundy,et al.  The Use of Explicit Plans to Guide Inductive Proofs , 1988, CADE.

[26]  Robert S. Boyer,et al.  Computational Logic , 1990, ESPRIT Basic Research Series.

[27]  W. Bledsoe,et al.  A precondition prover for analogy. , 1995, Bio Systems.

[28]  Roberto Coderschi The role of heuristics in automated theorem proving J.A Robinson's resolution principle , 1996 .

[29]  Alistair Knott,et al.  A data-driven methodology for motivating a set of coherence relations , 1996 .

[30]  Manfred Kerber,et al.  Proof Planning: A Practical Approach to Mechanized Reasoning in Mathematics , 1998 .

[31]  Robert L. Constable,et al.  Verbalization of High-Level Formal Proofs , 1999, AAAI/IAAI.

[32]  Ehud Reiter,et al.  Book Reviews: Building Natural Language Generation Systems , 2000, CL.

[33]  S. Ian Robertson,et al.  Problem-solving , 2001, Human Thinking.

[34]  Alan Bundy A Critique of Proof Planning , 2002, Computational Logic: Logic Programming and Beyond.

[35]  William McCune,et al.  Solution of the Robbins Problem , 1997, Journal of Automated Reasoning.

[36]  Graham Wrightson,et al.  An overview of automated reasoning and related fields , 2004, Journal of Automated Reasoning.

[37]  Siobhan Chapman Logic and Conversation , 2005 .

[38]  Geoff Sutcliffe,et al.  TPTP, TSTP, CASC, etc , 2007, CSR.

[39]  John Harrison,et al.  Handbook of Practical Logic and Automated Reasoning , 2009 .

[40]  Geoff Sutcliffe,et al.  The TPTP World - Infrastructure for Automated Reasoning , 2010, LPAR.

[41]  Alan Bundy,et al.  Automated theorem provers: a practical tool for the working mathematician? , 2011, Annals of Mathematics and Artificial Intelligence.

[42]  Jeremy Avigad,et al.  A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.