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Eliminating definitions and Skolem functions in first-order logic

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Jeremy AvigadAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 4, Issue 3

Pages 402 - 415

https://doi.org/10.1145/772062.772068

Published: 01 July 2003 Publication History

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Abstract

From proofs in any classical first-order theory that proves the existence of at least two elements, one can eliminate definitions in polynomial time. From proofs in any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions in polynomial time.

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Cited By

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HETZL S(2023)A SIMPLIFIED PROOF OF THE EPSILON THEOREMSThe Review of Symbolic Logic10.1017/S1755020323000217(1-16)Online publication date: 10-Jul-2023
https://doi.org/10.1017/S1755020323000217
Pakhomov FVisser A(2022)Finitely axiomatized theories lack self‐comprehensionBulletin of the London Mathematical Society10.1112/blms.1270854:6(2513-2531)Online publication date: 15-Jul-2022
https://doi.org/10.1112/blms.12708
Komara J(2022)Efficient elimination of Skolem functions in Archive for Mathematical Logic10.1007/s00153-021-00798-z61:3-4(503-534)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s00153-021-00798-z
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Index Terms

Eliminating definitions and Skolem functions in first-order logic
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
  2. 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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Reviews

Reviewer: Manuel Ojeda Aciego

A method to schedule offset free systems in a hard real-time context is presented in this paper. After characterizing tasks by their time parameters (period, deadline, requirement, offset), the author addresses the issue of computing the offsets of the tasks in an offset free environment, as opposed to a synchronous or asynchronous one. Experimental results are presented that show the validity of the proposed approach. The calculability and complexity of the proposed algorithms are also discussed throughout the paper, which indicate the author's desire to provide both a correct and an efficient method. The mathematical reasoning presented is rigorous, which supports the validity of the approach, but also sometimes makes the text difficult to read. The paper also includes many references to other authors, as well as to work previously published by the author himself. This might lead the reader to think that this is a final step in more global research, and that some pieces required for a global view of the proposed approach are missing. I would have appreciated some practical examples of systems where this approach could be beneficial. Online Computing Reviews Service

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 4, Issue 3

July 2003

121 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/772062

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2003

Published in TOCL Volume 4, Issue 3

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HETZL S(2023)A SIMPLIFIED PROOF OF THE EPSILON THEOREMSThe Review of Symbolic Logic10.1017/S1755020323000217(1-16)Online publication date: 10-Jul-2023
https://doi.org/10.1017/S1755020323000217
Pakhomov FVisser A(2022)Finitely axiomatized theories lack self‐comprehensionBulletin of the London Mathematical Society10.1112/blms.1270854:6(2513-2531)Online publication date: 15-Jul-2022
https://doi.org/10.1112/blms.12708
Komara J(2022)Efficient elimination of Skolem functions in Archive for Mathematical Logic10.1007/s00153-021-00798-z61:3-4(503-534)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s00153-021-00798-z
Chaudhuri KManighetti MMiller DMahboubi AMyreen M(2019)A proof-theoretic approach to certifying skolemizationProceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3293880.3294094(78-90)Online publication date: 14-Jan-2019
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Bienvenu MKikot SKontchakov RPodolskii VZakharyaschev M(2018)Ontology-Mediated QueriesJournal of the ACM10.1145/319183265:5(1-51)Online publication date: 29-Aug-2018
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Merz SVanzetto H(2018)Encoding TLA+ into unsorted and many-sorted first-order logicScience of Computer Programming10.1016/j.scico.2017.09.004158(3-20)Online publication date: Jun-2018
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Benedikt MCate BBoom M(2015)Effective Interpolation and Preservation in Guarded LogicsACM Transactions on Computational Logic10.1145/281457017:2(1-46)Online publication date: 6-Dec-2015
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ASCHIERI F(2015)Constructive forcing, CPS translations and witness extraction in Interactive realizabilityMathematical Structures in Computer Science10.1017/S096012951500046827:06(993-1031)Online publication date: 29-Oct-2015
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Benedikt MPuppis GVu H(2015)The complexity of higher-order queriesInformation and Computation10.1016/j.ic.2015.07.003244:C(172-202)Online publication date: 1-Oct-2015
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Baaz MHetzl SWeller D(2014)On the complexity of proof deskolemizationThe Journal of Symbolic Logic10.2178/jsl/133356664577:02(669-686)Online publication date: 12-Mar-2014
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Efficient elimination of Skolem functions in ${LK}^{h}$

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Efficient elimination of Skolem functions in LKh

Polymorphic lemmas and definitions in $\lambda$Prolog and Twelf

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Efficient elimination of Skolem functions in ${LK}^{h}$