Quati: An Automated Tool for Proving Permutation Lemmas

@inproceedings{Nigam2014QuatiAA,
  title={Quati: An Automated Tool for Proving Permutation Lemmas},
  author={Vivek Nigam and Giselle Reis and Leonardo Lima},
  booktitle={IJCAR},
  year={2014}
}
The proof of many foundational results in structural proof theory, such as the admissibility of the cut rule and the completeness of the focusing discipline, rely on permutation lemmas. It is often a tedious and error prone task to prove such lemmas as they involve many cases. This paper describes the tool Quati which is an automated tool capable of proving a wide range of inference rule permutations for a great number of proof systems. Given a proof system specification in the form of a theory… 

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References

SHOWING 1-10 OF 19 REFERENCES
Checking Proof Transformations with ASP
TLDR
The means to automatize the check of proof transformations by using Answer Set Prog ramming (ASP) are outlined.
From Proofs to Focused Proofs: A Modular Proof of Focalization in Linear Logic
TLDR
A new proof of the completeness of focused proofs in terms of proof transformation is given, first proved for MALL and then extended to full linear logic, and it is shown how the proof can be extended to larger systems, such as logics with induction.
An extended framework for specifying and reasoning about proof systems
TLDR
This paper shows how to extend the framework with subexponentials in order to declaratively encode a wider range of proof systems, including a number of non-trivial proof systems such as multi-conclusion intuitionistic logic, classical modal logic S4, intuitionistic Lax logic, and Negri’s labelled proof systems for different modal logics.
Logic Programming with Focusing Proofs in Linear Logic
TLDR
It is shown that the syntactic restriction induced by LinLog is not performed at the cost of any expressive power: a mapping from full linear logic to LinLog, preserving focusing proofs, and analogous to the normalization to clausal form for classical logic, is presented.
A Framework for Proof Systems
TLDR
It is shown that by providing different polarizations within a focused proof system for linear logic, one can account for natural deduction, sequent proofs, and tableaux proofs.
Algorithmic specifications in linear logic with subexponentials
TLDR
This work shows that focused proof search can be precisely linked to a simple algorithmic specification language that contains while-loops, conditionals, and insertion into and deletion from multisets and proposes a new logical connective that allows for the creation of new subexponentials, thereby further augmenting the algorithmic expressiveness of logic.
Subtractive logic
  • T. Crolard
  • Philosophy, Computer Science
    Theor. Comput. Sci.
  • 2001
On the Complexity of Linear Authorization Logics
  • Vivek Nigam
  • Computer Science, Mathematics
    2012 27th Annual IEEE Symposium on Logic in Computer Science
  • 2012
TLDR
This paper investigates the complexity of the provability problem, that is, determining whether a linear authorization logic formula is provable or not, and shows that the multiplicative propositional fragment of LAL is already undecidable in the presence of two principals.
Basic proof theory
TLDR
N- systems and H-systems and Gentzen systems, proof theory of arithmetic, second-order logic, and solutions to selected exercises.
Computer Science Logic
In the ambient logic of classical second order propositional calculus, we solve the specification problem for a family of excluded middle like tautologies. These are shown to be realized by
...
1
2
...