A System of Interaction and Structure III: The Complexity of BV and Pomset Logic

Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, a...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 19, Issue 4; no. 4
Main Authors: Nguyên, Lê Thành Dũng, Straßburger, Lutz
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 18.12.2023
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - logic in computer science
Logic in Computer Science
deep inference
series-parallel orders
proof nets
dicographs
system BV
seriesparallel orders
relation webs
pomset logic
cographs
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary:Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is $\Sigma_2^p$-complete. We also make some observations with respect to possible sequent systems for the two logics.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-19(4:25)2023