Proof, Abstraction and Semantics in Mathematics and Artificial Intelligence
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.
KeywordsMathematical Object Semantic Framework Automatic Proof Recent Program Logical Closure
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