Bunched implications

Author: mcjj

August undefined, 2024

Webby ﬁrst reformulating the traditional bunched sequent calculus using the simpler data-structure of nested sequents, following with a polarised and focused variant that we show is sound and complete via a cut-elimination argument. This establishes an operational semantics for focused proof-search in the logic of Bunched Implications. Webuse of bunched implications in this domain. However, the need for complex bunches in their proofs is rare at best. The question we ask is whether they are needed at all. This paper does not answer that question but it does lay out a foundation for using intuitionistic linear logic as opposed to bunched logic in automatic program veriﬁcation.

ILC: A Foundation for Automated Reasoning About Pointer …

WebAug 31, 2009 · The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two ... spinal investigation dorchester

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WebThe Logic of Bunched Implications (BI) [31] is well-known for its applications in systems modelling [32], especially a particular theory (of a variant of BI) called Separation Logic [37,23] which has found industrial use in program ver-i cation. In this work, we study an aspect of proof search in BI, relying on its WebJan 1, 2001 · We investigate the approach from the point of view of the logic BI of bunched implications of O'Hearnand Pym. We begin by giving a model in which the law of the excluded middleholds, thus showing that the approach is compatible with classical logic. The relationship between the intuitionistic and classical versions of the system is established ... WebDec 14, 2024 · We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to … spinal kinetics near me

A bunch of sessions: a propositions-as-sessions interpretation of ...

CiteSeerX — Resource models of bunched implications

WebMay 1, 2010 · The designs of accelerator systems that will be needed to transform Fermilab's Project X [1-3] into a high-power proton driver for a muon collider and/or a neutrino factory are discussed. These applications require several megawatts of beam power delivered in tens or hundreds of short multi-GeV bunches per second, respectively. WebMar 3, 2024 · The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications. As a consequence, contexts in the sequent presentation are not lists, nor multisets, but rather tree-like structures called bunches. This additional complexity notwithstanding, the logic … spinal kit contentsWebDec 14, 2024 · We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework for algebras arising... spinal joint dysfunction

"WebJan 1, 1998 · We introduce the logic of bunched implications, BI, in which multiplicative (or linear) and additive (or intuitionistic) implications live side-by-side. We provide a truth … " - Bunched implications

Bunched implications

[2202.01901] Bunched Fuzz: Sensitivity for Vector Metrics - arXiv.org

WebJan 1, 2002 · The logic of bunched implications (BI), introduced by O’Hearn and Pym, is a substructural logic which freely combines additive and multiplicative implications. WebMar 3, 2024 · The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications. As a consequence, contexts in the sequent presentation are not lists, nor multisets, but rather tree-like structures called bunches. This additional complexity notwithstanding, the logic …

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WebSep 20, 2024 · An Algebraic Glimpse at Bunched Implications and Separation Logic Peter Jipsen, Tadeusz Litak We overview the logic of Bunched Implications (BI) and … WebSemantic Cut Elimination for the Logic of Bunched Implications, Formalized in Coq. The logic of bunched implications (BI) is a substructural logic that for... 0 Dan Frumin, et al. ∙. share. research.

WebDec 10, 2024 · The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are mathematically involved, the formalization of important metatheoretical results is still incipient. In this … WebApr 13, 2024 · The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has...

WebThe original Fuzz products, tensor and with, correspond to the special cases L1 and L∞ . To simplify the handling of such products, we extend the Fuzz type system with bunches—as in the logic of bunched implications—where the distances of different groups of variables can be combined using different Lp distances. WebOct 16, 2024 · The logic of bunched implications, BI, provides a logical analysis of a basic notion of resource rich enough, for example, to form the logical basis for "pointer logic" and "separation logic ...

WebFeb 3, 2024 · Bunched Fuzz: Sensitivity for Vector Metrics. june wunder, Arthur Azevedo de Amorim, Patrick Baillot, Marco Gaboardi. Program sensitivity measures the distance between the outputs of a program when run on two related inputs. This notion, which plays a key role in areas such as data privacy and optimization, has been the focus of several …

WebOct 16, 2024 · The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof … spinal laser instituteWebThe logic of bunched implications (BI) [32] is an extension of intuitionistic logic with substructural connectives. BI (and its classical cousin Boolean BI) is known for, among other things, forming a basis for separation logic [31, 40] ś a pop-ular program logic for veriication of heap-manipulating spinal kyphosis disorderWebTHE LOGIC OF BUNCHED IMPLICATIONS PETER W. O'HEARN AND DAVID J. PYM Abstract. We introduce a logic BI in which a multiplicative (or linear) and an additive … spinal joints are severely inflamedWebSep 12, 2024 · We identify O'Hearn and Pym's Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called … spinal learning examplesWebPlayers to average 20 ppg, 5 rpg, 10 apg with a 60% ts%: Magic Johnson 3x, James Harden 3x (including this season), and Nikola Jokic this season. 154. 47. r/nba. spinal l4 and l5 problemsWebDec 3, 2010 · This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the monograph is also about informatics in a sense which I explain. Specifically, it... spinal kyphoplastyWeb2 days ago · April 10, 2024 Amy Henderson. It’s been a month now. When NASCAR levied penalties on a total of five teams and one additional driver after the March 12 United Rentals Work United 500 at Phoenix ... spinal junction