The ILLTP Library for Intuitionistic Linear Logic

Carlos Olarte
Valeria de Paiva
(Nuance Communications)
Elaine Pimentel
Giselle Reis

Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the traditional monograph "Introduction to Metamathematics". We analyze four different translations of intuitionistic logic into linear logic and compare their proofs using a linear logic based prover with focusing. In order to enhance the set of problems in our library, we apply the three provability-preserving translations to the propositional benchmarks in the ILTP Library. Finally, we generate a comprehensive set of reachability problems for Petri nets and encode such problems as linear logic sequents, thus enlarging our collection of problems.

In Thomas Ehrhard, Maribel Fernández, Valeria de Paiva and Lorenzo Tortora de Falco: Proceedings Joint International Workshop on Linearity & Trends in Linear Logic and Applications (Linearity-TLLA 2018), Oxford, UK, 7-8 July 2018, Electronic Proceedings in Theoretical Computer Science 292, pp. 118–132.
Published: 15th April 2019.

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