The ILLTP Library for Intuitionistic Linear Logic

  title={The ILLTP Library for Intuitionistic Linear Logic},
  author={Carlos Olarte and Valeria C V de Paiva and Elaine Pimentel and 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… 

Figures and Tables from this paper

Deriving Theorems in Implicational Linear Logic, Declaratively

Combinatorial generation of provable formulas of a given size, intuitionistic and linear logic theorem provers, theorems of the implicational fragment of propositional linear intuitionistic logic, Curry-Howard isomorphism, efficient generation of linear lambda terms in normal form, Prolog programs for lambda term generation and theorem proving.

Resourceful Program Synthesis from Graded Linear Types

This work provides two solutions to this resource management problem, adapting Hodas and Miller’s input-output model of linear context management to a graded modal linear type theory, and evaluates the performance of both approaches via their implementation as a program synthesis tool for the programming language Granule, which provides linear and gradedmodal typing.

Adversarial Learning to Reason in an Arbitrary Logic

This work proposes Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human knowledge or set of problems, and practically demonstrates the feasibility of the approach in multiple logical systems.

The ILTP Problem Library for Intuitionistic Logic

For the first time, the testing and evaluation of ATP systems for intuitionistic logic have been put on a firm basis by running comprehensive tests of currently available intuitionistic ATP systems on all problems in theILTP library.

TPTP and Beyond: Representation of Quantified Non-Classical Logics

Conservative extensions to the TPTP language are outlined that allow systematic syntax definitions for various expressive, non-classical logics, which are convinced that a standard syntax for prominent non- classical logic will not only facilitate their deployment but also support the development and comparability of corresponding theorem proving systems.

On concurrent behaviors and focusing in linear logic

Logic Programming with Focusing Proofs in Linear Logic

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.

Cut-Elimination for Full Intuitionistic Linear Logic

A different formal system is introduced describing the intuitionistic character of FILL and a full proof of the cut elimination theorem is provided.

The QMLTP Problem Library for First-Order Modal Logics

The Quantified Modal Logic Theorem Proving library provides a platform for testing and evaluating automated theorem proving systems for first-order modal logics and a small number of problems for multi-modal logic are included as well.

A Framework for Proof Systems

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.

Focusing and polarization in linear, intuitionistic, and classical logics

An Adequate Compositional Encoding of Bigraph Structure in Linear Logic with Subexponentials

The encoding of the bigraph structure is adequate and therefore the operations of composition and juxtaposition can be performed on the logical level and all the proof-theoretical tools of [Figure not available: see fulltext.] become available for querying and proving properties of bigraph structures.