Proof, Abstraction and Semantics in Mathematics and Artificial Intelligence

  • Bernard Meltzer
Part of the International Centre for Mechanical Sciences book series (CISM, volume 256)


The paradigm of a chain of inference from axioms is inadequate as an account of proof. A re-analysis of what proof is leads to a proposal for a semantic framework, which in a natural way accommodates abstraction, generalization and specialization involved in proof. It can be applied to other languages than that of mathematics, and in fact appears likely to be useful in considering the problems of free-ranging reasoning in programming languages of artificial intelligence.


Mathematical Object Semantic Framework Automatic Proof Recent Program Logical Closure 
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Copyright information

© Springer-Verlag Wien 1976

Authors and Affiliations

  • Bernard Meltzer
    • 1
  1. 1.School of Artificial Intelligence, Department of Computational LogicUniversity of EdinburghScotland

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