Quati: An Automated Tool for Proving Permutation Lemmas
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 in linear logic with subexponentials, Quati outputs in Open image in new window the permutation transformations for which it was able to prove correctness and also the possible derivations for which it was not able to do so. As illustrated in this paper, Quati’s output is very similar to proof derivation figures one would normally find in a proof theory book.
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- 3.Gelfond, M., Lifschitz, V.: Logic programs with classical negation. In: ICLP (1990)Google Scholar
- 4.Gentzen, G.: Investigations into logical deductions. The Collected Papers of Gerhard Gentzen (1969)Google Scholar
- 5.Herbrand, J.: Recherches sur la Théorie de la Démonstration. PhD thesis (1930)Google Scholar
- 6.Maehara, S.: Eine darstellung der intuitionistischen logik in der klassischen. Nagoya Mathematical Journal, 45–64 (1954)Google Scholar
- 8.Nigam, V., Pimentel, E., Reis, G.: An extended framework for specifying and reasoning about proof systems. Accepted to Journal of Logic and Computation, http://www.nigam.info/docs/modal-sellf.pdf
- 9.Nigam, V., Reis, G., Lima, L.: Quati: From linear logic specifications to inference rules (extended abstract). In: Brazilian Logic Conference, EBL (2014), http://www.nigam.info/docs/ebl14.pdf
- 10.Nigam, V.: On the complexity of linear authorization logics. In: LICS (2012)Google Scholar
- 11.Nigam, V., Miller, D.: Algorithmic specifications in linear logic with subexponentials. In: PPDP (2009)Google Scholar
- 13.Nigam, V., Reis, G., Lima, L.: Checking proof transformations with ASP. In: ICLP (Technical Communications) (2013)Google Scholar
- 14.Rauszer, C.: A formalization of the propositional calculus h-b logic. Studia Logica (1974)Google Scholar
- 15.Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory (1996)Google Scholar