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From Proofs to Focused Proofs: A Modular Proof of Focalization in Linear Logic [chapter]

Dale Miller, Alexis Saurin
Lecture Notes in Computer Science  
Andreoli proved this theorem for first-order linear logic 15 years ago. In the present paper, we give a new proof of the completeness of focused proofs in terms of proof transformation.  ...  The proof of this theorem is simple and modular: it is first proved for MALL and then is extended to full linear logic.  ...  We also want to thank the anonymous referees for their comments on a previous version of this paper. This work has been supported in part by INRIA through the "Equipes Associées" Slimmer.  ... 
doi:10.1007/978-3-540-74915-8_31 fatcat:erf6bfxqfbav5ptc23v4xo4xdq

Infinitary Proof Theory: the Multiplicative Additive Case

David Baelde, Amina Doumane, Alexis Saurin, Marc Herbstritt
2016 Annual Conference for Computer Science Logic  
It has appeared in the work of [3] on proof search and logic programming in linear logic, and is now recognized as one of the deep outcomes of linear logic, putting to the foreground the role of polarity  ...  Briefly, one can say that while proof nets have led to a better understanding of phenomena related to parallelism with proof-theoretical methods, polarities and focalization have led to a fine-grained  ...  Focalization graphs. Focused proofs are complete for proofs, not only provability: any linear proof is equivalent to a focused proof, up to cut-elimination.  ... 
doi:10.4230/lipics.csl.2016.42 dblp:conf/csl/BaeldeDS16 fatcat:vpem436twbaarpzosgwkng6kfu

Permutability in Proof Terms for Intuitionistic Sequent Calculus with Cuts

José Espírito Santo, Maria João Frade, Luís Pinto, Michael Wagner
2018 Types for Proofs and Programs  
normal proofs corresponds to a slight relaxation of focusing (in the sense of LJT).  ...  subsystems and the important subclasses of cut-free, normal, and focused proofs.  ...  Naturality and focusedness Natural proofs are a generalization of focused proofs (in the sense of LJT ).  ... 
doi:10.4230/lipics.types.2016.10 dblp:conf/types/SantoFP16 fatcat:gidb5qni2ba2fhq2j4jqkfuw5i

Wind sensing with drone-mounted wind lidars: proof of concept

Nikola Vasiljević, Michael Harris, Anders Tegtmeier Pedersen, Gunhild Rolighed Thorsen, Mark Pitter, Jane Harris, Kieran Bajpai, Michael Courtney
2020 Atmospheric Measurement Techniques  
We present a proof-of-concept (POC) drone–lidar system and report results from several test campaigns that demonstrate its ability to measure accurate wind speeds.  ...  The demonstration campaigns started with a series of comparisons of the wind speed measurements acquired by the POC system to simultaneous measurements performed by nearby mast-based sensors.  ...  The authors would like to express special gratitude to Michael Rassmussen (DTU), Claus Pedersen (DTU), and Per Hansen (DTU) for their help in setting up and operating the measurement system and Poul Hummelshøj  ... 
doi:10.5194/amt-13-521-2020 fatcat:b7wpcfnwtjb3tg3iolxt46orkm

Substructural Operational Semantics as Ordered Logic Programming

Frank Pfenning, Robert J. Simmons
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
The specifications exhibit a high degree of uniformity and modularity that allows us to analyze the structural properties required for each feature in isolation.  ...  We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forward-chaining operational interpretation.  ...  We would like to thank the anonymous reviewers for their comments, Jason Reed for a key insight in the proof of completeness, and Noam Zeilberger for pointing us to Laurent's unpublished note [9] .  ... 
doi:10.1109/lics.2009.8 dblp:conf/lics/PfenningS09 fatcat:4ou76lgejzazleihm2zqh7rzea

Proof-of-Concept of a Millimeter-Wave Integrated Heterogeneous Network for 5G Cellular

Shozo Okasaka, Richard Weiler, Wilhelm Keusgen, Andrey Pudeyev, Alexander Maltsev, Ingolf Karls, Kei Sakaguchi
2016 Sensors  
In this study, a proof-of-concept (PoC) was conducted to demonstrate the practicality of a prototype mmWave-integrated HetNet, using mmWave technologies for both backhaul and access.  ...  The use of the millimeter-wave (mmWave) spectrum is a key enabler to allowing 5G to achieve such enhancement in capacity.  ...  The authors would like to thank all participants who took part in the MiWEBA project.  ... 
doi:10.3390/s16091362 pmid:27571074 pmcid:PMC5038640 fatcat:jt4ntciujrg4dczh35oicddssq

Least and Greatest Fixed Points in Linear Logic [article]

David Baelde
2010 arXiv   pre-print
The resulting logic, which we call muMALL, satisfies two fundamental proof theoretic properties: we establish weak normalization for it, and we design a focused proof system that we prove complete.  ...  That second result provides a strong normal form for cut-free proof structures that can be used, for example, to help automate proof search.  ...  Given a mapping from intuitionistic to linear logic, and a complete focused proof system for linear logic, one can often build a complete focused proof-system for intuitionistic logic. ⊢ F / / ⊢ [F ] ⊢  ... 
arXiv:0910.3383v4 fatcat:3znfpcjtd5e5rfoffvxkltibyq

Axiom Directed Focusing [chapter]

Clément Houtmann
2009 Lecture Notes in Computer Science  
In particular we prove a focalization theorem for cut-free superdeduction modulo: we show that permutations of inference rules can transform any cut-free proof in deduction modulo into a cut-free proof  ...  Superdeduction and deduction modulo are methods specially designed to ease the use of first-order theories in predicate logic.  ...  Many thanks also to Richard Bonichon and Cody Roux for fertile discussions, to anonymous referees for their comments on a previous version of this paper, to the Modulo meetings and to the Pareo team for  ... 
doi:10.1007/978-3-642-02444-3_11 fatcat:ex67vbd6jjfzbh54oiwvhieula

Multi-Focusing on Extensional Rewriting with Sums

Gabriel Scherer, Marc Herbstritt
2015 International Conference on Typed Lambda Calculus and Applications  
It relies on maximally multi-focused proofs, a notion of canonical derivations introduced for linear logic.  ...  Lindley's rewriting closely corresponds to preemptive rewriting [CMS08], a technical device used in the meta-theory of maximal multi-focus.  ...  Acknowledgements The author thanks his advisor, Didier Rémy, for his directions and advice, and for the freedom of making an overly long detour through the proof search literature; Alexis Saurin for his  ... 
doi:10.4230/lipics.tlca.2015.317 dblp:conf/tlca/Scherer15 fatcat:epwdawnvgjhxpojczyrb56cqq4

Introduction

Martin Giese, Andrew Ireland, Laura Kovács
2010 Journal of symbolic computation  
Like the work of Luo, Craciun, Qin and He, this paper promotes a modular approach to verification.  ...  Based upon constraint solving, their interpolation algorithm focuses on the combined theory of linear arithmetic and uninterpreted function symbols.  ... 
doi:10.1016/j.jsc.2010.06.002 fatcat:5bfwjcy6q5fetdjdaticlnfhmu

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
In literature, there is a shortage of comprehensive documents that can provide proper guidance about the preferences of theorem provers with respect to their designs, performances, logical frameworks,  ...  In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these tools.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ... 
arXiv:1912.03028v1 fatcat:fabxqg75xjhxlh7u3uyypgyzdy

Linear Contexts, Sharing Functors: Techniques for Symbolic Computation [chapter]

Gérard Huet
2003 Applied Logic Series  
We present in this paper two design issues concerning fundamental representation structures for symbolic and logic computations.  ...  This may be considered a disciplined use of pointer reversal techniques.  ...  The author wishes to thank the referees of this paper, who made interesting suggestions leading to an improved presentation of the material.  ... 
doi:10.1007/978-94-017-0253-9_4 fatcat:nhaqrstcpvctpenp6tkvjxnv7e

Belief functions on lattices [article]

Michel Grabisch
2008 arXiv   pre-print
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set  ...  of properties according to our needs.  ...  The inverse formula, giving m in terms of bel, has to be computed from (3) , and depends only on the structure of L.  ... 
arXiv:0811.3373v1 fatcat:dlbll7sut5cefips6lcgbyplia

Belief functions on lattices

Michel Grabisch
2009 International Journal of Intelligent Systems  
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set  ...  of properties according to our needs.  ...  The inverse formula, giving m in terms of bel, has to be computed from (3) , and depends only on the structure of L.  ... 
doi:10.1002/int.20321 fatcat:dzkgxjqcqvdphid52w2kif5dlq

Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General

Ross T. Brady
2017 IfColog journal of logics and their applications (FLAP)  
To make a long story short, we took the salient word from the long title of the project to create a short catchy brand for the workshop.  ...  The "third place" refers to the third argument place of a three-place relation, specifically, the third argument place of the ternary accessibility relation in the semantics of relevance logics.  ...  Their careful reading of a previous version of this paper helped to make it a much better final text.  ... 
dblp:journals/flap/Brady17 fatcat:dbhyqmbfczc43c2kwnxbrh4lv4
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