INTRODUCTION TO SEMI-AUTOMATED MATHEMATICS.

Abstract

The subject of this report is mechanical theorem proving, and in it are described two computer programs that represent an approach different from the usual ones based on the Herbrand Theorem in which the computer unaided seeks to construct proofs. In the approach described here, non algorithmic proof procedures are employed and the basic function of the computer is to render as much assistance as possible to the mathe matician in specifying such procedures. To aid in this function, two programming languages and associated processors have been written that pro vide a logical language, closely resembling the language of mathematical logic, for specifying to the computer exact procedures for building proofs in the propositional calculus and first order axioms systems. One language is based on a natural deduction formulation of the proposi tional calculus, and the other on an axiomatic formulation of any first-order axiom system such as elementary group theory and set theory. Among the provisions of the latter language is a com mand for generating the most general relevant substitution instances of axioms and theorems already proved. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 15, 1963
Accession Number
AD0413929

Entities

People

  • James H. Bennett
  • James R. Guard
  • Thomas H. Mott Jr.
  • William B. Easton

Tags

DTIC Thesaurus Topics

  • Calculus
  • Computer Programming
  • Computer Programs
  • Computers
  • Language
  • Logic
  • Mathematical Analysis
  • Mathematical Logic
  • Mathematics
  • Programming Languages
  • Set Theory
  • Theorems

Readers

  • Computational Linguistics
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design