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Notes Towards a Semantics for Proof-search

✍ Scribed by David J. Pym

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
156 KB
Volume
37
Category
Article
ISSN
1571-0661

No coin nor oath required. For personal study only.

✦ Synopsis

Algorithmic proof-search is an essential enabling technology throughout informatics. Proof-search is the proof-theoretic realization of the formulation of logic not as a theory of deduction but rather as a theory of reduction. Whilst deductive logics typically have a well-developed semantics of proofs, reductive logics are typically well-understood only operationally. Each deductive system can, typically, be read as a corresponding reductive system. We discuss some of the problems which must be addressed in order to provide a semantics of proof-searches of comparable value to the corresponding semantics of proofs. Just as the semantics of proofs is intimately related to the model theory of the underlying logic, so too should be the semantics of proof-searches. We discuss how to solve the problem of providing a semantics for proof-searches which adequately models both operational and logical aspects of the reductive system. Pym Ξ¦ β‡’ Ξ“ Ο† ' E [Ξ“] [Ξ¦] : [Ο†] s d d d d d Β©

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