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Computer Science > Logic in Computer Science

arXiv:2107.07661v1 (cs)
[Submitted on 16 Jul 2021 (this version), latest version 8 Aug 2021 (v2)]

Title:Facilitating Meta-Theory Reasoning (Invited Paper)

Authors:Giselle Reis (Carnegie Mellon University)
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Abstract:Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be designed as a set of rules such that proofs using those rules are correct by construction. Therefore, one must consider all ways these rules can interact and prove that they satisfy certain properties which makes them "well-behaved". This is called the meta-theory of a proof system.
Meta-theory proofs typically involve many cases on structures with lots of symbols. The majority of cases are usually quite similar, and when a proof fails, it might be because of a sub-case on a very specific configuration of rules. Developing these proofs by hand is tedious and error-prone, and their combinatorial nature suggests they could be automated.
There are various approaches on how to automate, either partially or completely, meta-theory proofs. In this paper, I will present some techniques that I have been involved in for facilitating meta-theory reasoning.
Comments: In Proceedings LFMTP 2021, arXiv:2107.07376
Subjects: Logic in Computer Science (cs.LO)
ACM classes: F.4.1
Cite as: arXiv:2107.07661 [cs.LO]
  (or arXiv:2107.07661v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2107.07661
Journal reference: EPTCS 337, 2021, pp. 1-12
Related DOI: https://doi.org/10.4204/EPTCS.337.1

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Fri, 16 Jul 2021 01:43:52 UTC (21 KB)
[v2] Sun, 8 Aug 2021 02:10:30 UTC (21 KB)
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