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An analysis of (linear) exponentials based on extended sequents

S Guerrini
1998 Logic Journal of the IGPL  
We apply the 2-sequents approach to the analysis of several logics derived from linear logic.  ...  Comments Abstract: We apply the 2-sequents approach to the analysis of several logics derived from linear logic.  ...  A 2-sequent is an expression`;, w h e r e ; is a 2-sequence in which at least one of the i is not empty. Informally, l e v els express a form of modal (exponential) dependency.  ... 
doi:10.1093/jigpal/6.5.735 fatcat:vkd5mqlgtfbqvaw7whpk72zzba

Focused Linear Logic and the λ-calculus

Taus Brock-Nannestad, Nicolas Guenot
2015 Electronical Notes in Theoretical Computer Science  
, and their variants based on sequent calculi.  ...  However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus.  ...  Acknowledgement The authors would like to thank the anonymous reviewers for their helpful and thorough comments on a previous draft.  ... 
doi:10.1016/j.entcs.2015.12.008 fatcat:kgvhqmfigrdpngubcf3lfcfd54

Linear Logic Properly Displayed [article]

Giuseppe Greco, Alessandra Palmigiano
2016 arXiv   pre-print
Our proposal builds on an algebraic and order-theoretic analysis of linear logic, and applies the guidelines of the multi-type methodology in the design of display calculi.  ...  Based on the same design, we introduce a variant of Lambek calculus with exponentials, aimed at capturing the controlled application of exchange and associativity.  ...  The possibility of appealing to the general multi-type methodology in the specific case of linear logic is justified by an analysis of the algebraic semantics of linear logic, aimed at identifying the  ... 
arXiv:1611.04181v1 fatcat:hdhlj5elvnfrzf6xuy7egi6yqy

The logic of linear functors

R. BLUTE, J. R. B. COCKETT, R. A. G. SEELY
2002 Mathematical Structures in Computer Science  
the particular case when the logics are based on a linear functor, to give a de nite presentation of these ideas.  ...  This paper describes a family of logics whose categorical semantics is based on functors with structure rather than on categories with structure.  ...  We have also noted that our logic LF can provides an alternative sequent calculus for the analysis of Retor e's noncommutative connective on coherence spaces.  ... 
doi:10.1017/s0960129502003717 fatcat:fsqzlfblfzf7bbyamgio5ijshy

On noncommutative extensions of linear logic [article]

Sergey Slavnov
2019 arXiv   pre-print
We introduce decorated sequents, which are sequents equipped with an extra structure of a binary relation of reachability on formulas.  ...  Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus.  ...  The system BV was subsequently extended [GS11] to accommodate linear logic exponentials, an extension with additive connectives was considered as well [Hor15] .  ... 
arXiv:1703.10092v5 fatcat:diuxa5cfvvgpdpnurj6jdio6fy

Linearizing intuitionistic implication

Patrick Lincoln, Andre Scedrov, Natarajan Shankar
1993 Annals of Pure and Applied Logic  
An embedding of the implicational propositional intuitionistic logic (IIL) into the nonmodal fragment of intuitionistic linear logic (IMALL) is given.  ...  Shankar, Linearizing intuitionistic implication, Annals of Pure and Applied Logic 60 (1993) 151-177.  ...  An interesting aspect of cut-elimination is that in linear logic it is possible to encode constraints on the form of a cut-free proof in the conclusion sequent.  ... 
doi:10.1016/0168-0072(93)90041-b fatcat:bczpla63ijclhnkfdhegaywyim

Linear Logic and Strong Normalization

Beniamino Accattoli, Marc Herbstritt
2013 International Conference on Rewriting Techniques and Applications  
It is the first proof of strong normalization for MELL which does not rely on any form of confluence, and so it smoothly scales up to full linear logic.  ...  The insight indeed comes from the theory of explicit substitutions, and from looking at the exponentials as a substitution device.  ...  Acknowledgements To Delia Kesner, who taught me the art of strong normalization proofs, and with whom I had uncountable discussions on commutative rules, normalization, and proof nets.  ... 
doi:10.4230/lipics.rta.2013.39 dblp:conf/rta/Accattoli13 fatcat:niytow7rsbhuxabwthipfbwlti

The ILLTP Library for Intuitionistic Linear Logic

Carlos Olarte, Valeria de Paiva, Elaine Pimentel, Giselle Reis
2019 Electronic Proceedings in Theoretical Computer Science  
We analyze four different translations of intuitionistic logic into linear logic and compare their proofs using a linear logic based prover with focusing.  ...  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.  ...  For an initial experiment with this first proposed set of sequents, we implemented a focused-based prover for ILL.  ... 
doi:10.4204/eptcs.292.7 fatcat:hdwnb3hccjevlmfucibkx2vcni

The Linear Logical Abstract Machine

Eduardo Bonelli
2006 Electronical Notes in Theoretical Computer Science  
We derive an abstract machine from the Curry-Howard correspondence with a sequent calculus presentation of Intuitionistic Propositional Linear Logic.  ...  Transformation of natural deduction proofs into our sequent calculus yields a typepreserving compilation function from the Linear Lambda Calculus to the abstract machine.  ...  ) A&B, or an exponential ("!"  ... 
doi:10.1016/j.entcs.2006.04.007 fatcat:p3qwvmnw4zghjjbdjictiwabk4

Computational Complexity of Deciding Provability in Linear Logic and its Fragments [article]

Florian Chudigiewitsch
2021 arXiv   pre-print
We prove an original complexity characterization of a fragment of the logic and present ideas for a new, structural approach to the examination of provability in linear logic.  ...  We present the current state of the complexity-theoretic characterization of the most important fragments of linear logic.  ...  "On the expressivity of elementary linear logic: Characterizing Ptime and an exponential time hierarchy".  ... 
arXiv:2110.00562v1 fatcat:a6sidawnbjh5jpf2cvrermfrcy

Specifying Proof Systems in Linear Logic with Subexponentials

Vivek Nigam, Elaine Pimentel, Giselle Reis
2011 Electronical Notes in Theoretical Computer Science  
However, some systems that impose more complicated structural restrictions on its sequents cannot be easily captured in linear logic, since it only distinguishes two types of formulas: classical and linear  ...  This work shows that one can encode a wider range of proof systems by using focused linear logic with subexponentials.  ...  The result was based on the fact that cut elimination is often proved via case analysis, where the duality of inference rules play an important role in the elimination of non-atomic cuts.  ... 
doi:10.1016/j.entcs.2011.03.009 fatcat:wyzvjdecyvaebolnebwgliih6i

Linear logic, coherence and dinaturality

Richard Blute
1993 Theoretical Computer Science  
Thus, the dinatural approach to modelling polymorphic types, due to Bainbridge et al. 119901, can be extended to linear polymorphism.  ...  An autonomous deductive system is a deductive system with several added features. which are suggested by the properties of proof nets.  ...  Acknowledgment This paper is a revised version of the author's thesis, written at the University of Pennsylvania.  ... 
doi:10.1016/0304-3975(93)90053-v fatcat:edbz3igdkjbv7ny2qdp3sukncy

A Matrix Characterization for Multiplicative Exponential Linear Logic

Christoph Kreitz, Heiko Mantel
2004 Journal of automated reasoning  
We develop a matrix characterization of logical validity in MELL, the multiplicative fragment of propositional linear logic with exponentials and constants.  ...  Our characterization is based on concepts similar to matrix characterizations proposed by Wallen for other non-classical logics.  ...  Acknowledgments We would like to thank Marcelo Correa for his useful feedback on the soundness and completeness proofs in Section 6.  ... 
doi:10.1023/b:jars.0000029976.22387.ac fatcat:iw2ki256vjf6xfocfayaxwytgi

Object calculi in linear logic

M Bugliesi
2000 Journal of Logic and Computation  
We show that a complete semantic account of these features may be given in a fragment of higher-order linear logic.  ...  Several calculi of objects have been studied in the recent literature, that support the central features of object-based languages: messages, inheritance, dynamic dispatch, object update and object-extension  ...  The revised version of this paper was written while the first author was visiting the Max-Planck-Institut für Informatik. He would like to thank Prof.  ... 
doi:10.1093/logcom/10.1.75 fatcat:m6pqyugctfeglgpmmjra77hvma

Interaction Graphs: Full Linear Logic [article]

Thomas Seiller
2016 arXiv   pre-print
Adapting older constructions by Girard, one can clearly define "full" exponentials, but at the cost of these quantitative features.  ...  Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect.  ...  Hj Continuous Dialects Interaction graphs models dealing with exponential connectives of linear logic are based on the notion of thick and sliced graphings, obtained by a second layer of generalisation  ... 
arXiv:1504.04152v2 fatcat:jtt4a3usxrfz7la44doum7mpzq
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