The ILLTP Library for Intuitionistic Linear Logic

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

Implementing tableaux by decision diagrams

Binary Decision Diagrams (BDDs) are usually thought of as devices engineered specially for classical propositional logic. We show that we can build on one of their variants, Minato\u27s zero-suppressed BDDs, to build compact data structures that encode whole tableaux. We call these structures tableaux decision diagrams (TDDs), and show how tableaux proof search is implemented in this framework. For this to be efficient, we have to restrict to canonical proof formats (in the sense of Galmiche et al.) to be able to take advantage of sharing in TDDs. Sharing is fundamental, not because it reduces memory consumption, but because it allows us to expand or close many tableaux paths in parallel, with corresponding gains in efficiency. We provide some empirical evidence that this is indeed efficient, by illustrating the method on a well-chosen system for propositional intuitionistic logic

Foundations of Proof Search Strategies Design in Linear Logic

In this paper, we investigate automated proof construction in classical linear logic (CLL) by giving logical foundations for the design of proof search strategies. We propose common theoretical foundations for top-down, bottom-up and mixed proof search procedures with a systematic formalization of strategies construction using the notions of immediate or chaining composition or decomposition, deduced from permutability properties and inference movements in a proof. Thus, we have logical bases for the design of proof strategies in CLL fragments and then we can propose sketches for their design