research-article

Permissive-nominal logic

Authors:

Murdoch J. GabbayAuthors Info & Claims

PPDP '10: Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming

Pages 165 - 176

https://doi.org/10.1145/1836089.1836111

Published: 26 July 2010 Publication History

Abstract

Permissive-Nominal Logic (PNL) is an extension of first-order logic where term-formers can bind names in their arguments.

This allows for direct axiomatisations with binders, such as the ∀l-quantifier of first-order logic itself and the λ-binder of the lambda-calculus. This also allows us to finitely axiomatise arithmetic.

Like first- and higher-order logic and unlike other nominal logics, equality reasoning is not necessary to alpha-rename.

All this gives PNL much of the expressive power of higher-order logic, but terms, derivations and models of PNL are first-order in character, and the logic seems to strike a good balance between expressivity and simplicity.

References

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Index Terms

Permissive-nominal logic
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Logic
    1. Proof theory

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cover image ACM Other conferences

PPDP '10: Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming

July 2010

266 pages

ISBN:9781450301329

DOI:10.1145/1836089

Conference Chairs:
Temur Kutsia
RISC, Johannes Kepler University Linz, Austria
,
Wolfgang Schreiner
RISC, Johannes Kepler University Linz, Austria
,
Program Chair:
Maribel Fernández
King's College London, UK

Copyright © 2010 ACM.

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Johannes Kepler University, Linz, Austria
SIGPLAN: ACM Special Interest Group on Programming Languages

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 July 2010

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PPDP '10

PPDP '10: Principles and Practice of Declarative Programming

July 26 - 28, 2010

Hagenberg, Austria

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PPDP '10 Paper Acceptance Rate 21 of 57 submissions, 37%;

Overall Acceptance Rate 230 of 486 submissions, 47%

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