Mathematical Reasoning with Diagrams. From Intuition to Automation

Note moyenne 
Mateja Jamnik - .
Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems that humans can prove by the... Lire la suite
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Résumé

Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems that humans can prove by the use of geometric operations on diagrams, so-called diagrammatic proofs. This book investigates and describes how such diagrammatic reasoning about mathematical theorems can be automated. Concrete, rather than general, diagrams are used to prove particular instances of a universal statement. The " inference steps " of a diagrammatic proof are formulated in terms of geometric operations on the diagram. A general schematic proof of the universal statement is induced from these proof instances by means of the constructive w-rule. Schematic proofs are represented as recursive programs, which when given a particular diagram return a proof for that diagram. It is necessary to reason about this recursive program to show that it outputs a correct proof. One method of confirming the soundness of the abstraction of a schematic proof from proof instances is to prove the correctness of the schematic proof in the meta-theory of diagrams. This book presents an investigation of these ideas and their implementation in a system called DIAMOND.

Sommaire

    • The History of Diagrammatic Systems
    • Diagrammatic Theorems and the Problem Domain
    • The Constructive w-Rule and Schematic Proofs
    • Designing a Diagrammatic Reasoning System
    • Diagrammatic Operations
    • The Construction of Schematic Proofs
    • The Verification of Schematic Proofs
    • Diamond in Action
    • Complete Automation.

Caractéristiques

  • Date de parution
    05/02/2002
  • Editeur
  • Collection
  • ISBN
    1-57586-324-3
  • EAN
    9781575863245
  • Présentation
    Broché
  • Nb. de pages
    204 pages
  • Poids
    0.31 Kg
  • Dimensions
    15,4 cm × 23,0 cm × 1,2 cm

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