Deep inference and expansion trees for second-order multiplicative linear logic

Straßburger, Lutz

doi:10.1017/s0960129518000385

Cited by 3 publications

(2 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof The simplest way to prove this is using the sequentialization result of Retoré [26] together with the correspondence between sequent calculus and deep inference [14]. A direct sequentialization from proof nets to deep inference derivations can be found in [30].…”

Section: Multiplicative Flowsmentioning

confidence: 99%

Combinatorial Flows as Bicolored Atomic Flows

Omidvar

Straßburger

2022

Logic, Language, Information, and Computation

Self Cite

View full text Add to dashboard Cite

We introduce combinatorial flows as a graphical representation of proofs. They can be seen as a generalization of atomic flows on one side and of combinatorial proofs on the other side. From atomic flows, introduced by Guglielemi and Gundersen, they inherit the close correspondence with open deduction and the possibility of tracing the occurrences of atoms in a derivation. From combinatorial proofs, introduced by Hughes, they inherit the correctness criterion that allows to reconstruct the derivation from the flow. In fact, combinatorial flows form a proof system in the sense of Cook and Reckhow. We show how to translate between open deduction derivations and combinatorial flows, and we show how they are related to combinatorial proofs with cuts.

show abstract

Section: Multiplicative Flowsmentioning

confidence: 99%

Combinatorial Flows as Bicolored Atomic Flows

Omidvar

Straßburger

2022

Logic, Language, Information, and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Remark 39. Note that it is also possible to do a direct "sequentialization" into the deep inference system MLS1 X , using the techniques presented in [38] and [46].…”

Section: From Fonets To Mls1 X Proofsmentioning

confidence: 99%

Combinatorial Proofs and Decomposition Theorems for First-order Logic

Hughes

Straßburger

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a syntax-free presentation of a proof that is independent from any set of inference rules. We show that the two proof representations are related via a deep inference decomposition theorem that establishes a new kind of normal form for syntactic proofs. This yields (a) a simple proof of soundness and completeness for firstorder combinatorial proofs, and (b) a full completeness theorem: every combinatorial proof is the image of a syntactic proof.

show abstract