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The Logic Theorist proves theorems by search

Newell, Simon, and Shaw's program finds a shorter proof than Russell and Whitehead's own

On the timeline · around 1956 · Symbolic AI, Booms and WintersFoundationsSymbolic AI, Booms and WintersThe Logic Theorist proves theorems by search195219541956196019641968

Quick facts

Researchers
Allen Newell, Herbert Simon, J. C. Shaw
Institution
RAND Corporation
Result
Proved 38 of 52 Principia Mathematica theorems

What happened

Allen Newell, Herbert Simon, and Cliff Shaw, working at the RAND Corporation, built the Logic Theorist to prove theorems from Whitehead and Russell's Principia Mathematica. Before any code ran on a machine, the team simulated the program by hand, with Simon's family members acting out the roles of individual program components using index cards. Once running on the JOHNNIAC computer, the program worked backward from a theorem to be proved, searching through chains of logical rules and past results to find a valid derivation, an approach the team called heuristic search rather than exhaustive checking. It went on to prove 38 of the first 52 theorems in chapter two of Principia Mathematica, including one for which its proof was shorter and more elegant than the original by Russell and Whitehead.

Why it matters

The Logic Theorist introduced heuristic search, list processing, and the idea of reasoning as a search through a space of possibilities, concepts that became standard tools across symbolic AI for the next three decades.

How we know

The Computer History Museum and the ACM's biography of Newell, co-written for his Turing Award, both document the RAND collaboration, the hand-simulation, and the theorem-proving results.

Sources

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