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Algorithmic specifications in linear logic with subexponentials

Vivek Nigam, Dale Miller
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
In addition, we propose a new logical connective that allows for the creation of new subexponentials, thereby further augmenting the algorithmic expressiveness of logic.  ...  Treating locations as subexponentials greatly increases the algorithmic expressiveness of logic.  ...  Conclusions In this paper, we show that a wide range of algorithms can be specified in the linear logic system with subexponentials called SELL.  ... 
doi:10.1145/1599410.1599427 dblp:conf/ppdp/NigamM09 fatcat:2xzv7s5wlzh4polnubupd6divq

Specifying Proof Systems in Linear Logic with Subexponentials

Vivek Nigam, Elaine Pimentel, Giselle Reis
2011 Electronical Notes in Theoretical Computer Science  
This work shows that one can encode a wider range of proof systems by using focused linear logic with subexponentials.  ...  Due to linear logic's finer control on structural rules, it is possible to match the structural restrictions specified in the encoded logic with the use of linear logic connectives.  ...  Focused linear logic system with subexponentials.  ... 
doi:10.1016/j.entcs.2011.03.009 fatcat:wyzvjdecyvaebolnebwgliih6i

Quati: An Automated Tool for Proving Permutation Lemmas [chapter]

Vivek Nigam, Giselle Reis, Leonardo Lima
2014 Lecture Notes in Computer Science  
Given a proof system specification in the form of a theory in linear logic with subexponentials, Quati outputs in L A T E X the permutation transformations for which it was able to prove correctness and  ...  As illustrated in this paper, Quati's output is very similar to proof derivation figures one would normally find in a proof theory book.  ...  ) to derivations in linear logic with subexponentials.  ... 
doi:10.1007/978-3-319-08587-6_18 fatcat:ym2kxrefqrgylh7agegchqrgvy

Subexponentials in non-commutative linear logic [article]

Max Kanovich, Stepan Kuznetsov, Vivek Nigam, Andre Scedrov
2017 arXiv   pre-print
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics.  ...  We also obtain some new undecidability and decidability results on non-commutative linear logic with subexponentials.  ...  Cyclic Linear Logic with Subexponentials In this section we define the second calculus considered in this paper, the extension of cyclic linear logic [Yetter, 1990] with subexponentials.  ... 
arXiv:1709.03607v1 fatcat:ft5zuquzsza25a3csdz6hxxqhe

Facilitating Meta-Theory Reasoning (Invited Paper)

Giselle Reis
2021 Electronic Proceedings in Theoretical Computer Science  
Meta-theory proofs typically involve many cases on structures with lots of symbols.  ...  In this paper, I will present some techniques that I have been involved in for facilitating meta-theory reasoning.  ...  (Subexponential) Linear Logic Linear logic is a refinement of classical logic in the sense that it allows a finer control over structural rules.  ... 
doi:10.4204/eptcs.337.1 fatcat:dobvkljpbraxfgyc5qtbdwoufq

Soft Subexponentials and Multiplexing [chapter]

Max Kanovich, Stepan Kuznetsov, Vivek Nigam, Andre Scedrov
2020 Lecture Notes in Computer Science  
One of the subexponentials allows the multiplexing rule in the style of soft linear logic and light linear logic. The second subexponential provides the exchange rule.  ...  Linear logic and its refinements have been used as a specification language for a number of deductive systems.  ...  12] subexponentials, light linear logic [7] , soft linear logic [16] , and easy linear logic [10] .  ... 
doi:10.1007/978-3-030-51074-9_29 fatcat:rx3qbmznpzdh7fme4xiv27bqgu

Classical and Intuitionistic Subexponential Logics are Equally Expressive [article]

Kaustuv Chaudhuri
2010 arXiv   pre-print
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic  ...  We show here that subexponential logic, which is a family of substructural refinements of classical logic, each parametric over a preorder over the subexponential connectives, does not suffer from this  ...  As particular instances, we obtain focal adequacy results for: classical logic (CL) in intuitionistic logic (IL), IL in classical linear logic (CLL), CLL in intuitionistic linear logic (ILL), and an indefinite  ... 
arXiv:1006.3134v1 fatcat:mlzrr7v4ajb7nm5h2nfpbhnswi

Classical and Intuitionistic Subexponential Logics Are Equally Expressive [chapter]

Kaustuv Chaudhuri
2010 Lecture Notes in Computer Science  
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic  ...  We show here that subexponential logic, which is a family of substructural refinements of classical logic, each parametric over a preorder over the subexponential connectives, does not suffer from this  ...  As particular instances, we obtain focal adequacy results for: classical logic (CL) in intuitionistic logic (IL), IL in classical linear logic (CLL), CLL in intuitionistic linear logic (ILL), and an indefinite  ... 
doi:10.1007/978-3-642-15205-4_17 fatcat:2wu4xiliovdatgokl2mb6abzva

An extended framework for specifying and reasoning about proof systems

Vivek Nigam, Elaine Pimentel, Giselle Reis
2014 Journal of Logic and Computation  
Finally, we have implemented a tool, described in Section 6, that accepts a linear logic with subexponentials specification and automatically checks whether principals cuts can be reduced to atomic cuts  ...  First, in Section 4, we demonstrate how to declaratively specify proof systems with more involved structural and logical inferences rules using linear logic theories with subexponentials.  ...  We are also grateful to Kaustuv Chaudhuri for pointing out an error in a previous version of this paper.  ... 
doi:10.1093/logcom/exu029 fatcat:uontgaw6gbfh3mcyxzpgdc7jqu

An Adequate Compositional Encoding of Bigraph Structure in Linear Logic with Subexponentials [chapter]

Kaustuv Chaudhuri, Giselle Reis
2015 Lecture Notes in Computer Science  
with subexponentials (SEL).  ...  In linear logic, formulas can be split into two sets: classical (those that can be used as many times as necessary) or linear (those that are consumed and no longer available after being used).  ...  Background Subexponential Logic (SEL) Subexponential logic (SEL) is a variant of linear logic with a family of exponential connectives-called subexponentials (a term coined in [12] )-that are indexed  ... 
doi:10.1007/978-3-662-48899-7_11 fatcat:g2twkmcfrjdmbkjdi7s3ri27by

Verification of Spatial and Temporal Modalities in Biochemical Systems

Davide Chiarugi, Moreno Falaschi, Diana Hermith, Carlos Olarte
2015 Electronical Notes in Theoretical Computer Science  
For that, we use as specification language a fragment of intuitionistic linear logic with subexponentials (SELL).  ...  in the pathway.  ...  Linear Logic with Subexponentials Linear logic (LL) with subexponentials (SELL) [23] shares with LL [30] all its connectives except the exponentials ! and ?.  ... 
doi:10.1016/j.entcs.2015.06.009 fatcat:ksphyjbd5fbqheyjhhoiyoy72a

A framework for linear authorization logics

Vivek Nigam
2014 Theoretical Computer Science  
Linear authorization logics (LALs) are logics based on linear logic that can be used for modeling effect-based authentication policies.  ...  This paper investigates the complexity of the provability problem, that is, determining whether a formula is provable in a linear authorization logic.  ...  Linear Logic with Subexponentials Besides sharing all connectives with linear logic, SELL may include as many exponential-like connectives, called subexponentials, as one needs.  ... 
doi:10.1016/j.tcs.2014.02.018 fatcat:22pxpnai5vflfhhq6sv6wmwvbi

On the Complexity of Linear Authorization Logics

Vivek Nigam
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
Linear authorization logics (LAL) are logics based on linear logic that can be used for modeling effect-based authentication policies.  ...  This paper investigates the complexity of the provability problem, that is, determining whether a linear authorization logic formula is provable or not.  ...  The system for classical linear logic with subexponentials was proposed in [7] and further investigated in [23] .  ... 
doi:10.1109/lics.2012.61 dblp:conf/lics/Nigam12 fatcat:mpujo73eovhhjaosobmvkr273a

Combinatorial structure and randomized subexponential algorithms for infinite games

Henrik Björklund, Sergei Vorobyov
2005 Theoretical Computer Science  
In this setting, we suggest randomized subexponential algorithms appropriate for RLG-and PRLG-function optimization.  ...  We show that the subexponential algorithms for combinatorial linear programming, due to Kalai and Matoušek, Sharir, Welzl, can be adapted for optimizing the RLG-and PRLG-functions.  ...  In this abstract setting, we show that the subexponential, randomized algorithms for linear programming due to Kalai [26] and Matoušek et al.  ... 
doi:10.1016/j.tcs.2005.07.041 fatcat:u3gsujjxkjflzfu5ndcr6cgqru

Cyclic games and linear programming

Sergei Vorobyov
2008 Discrete Applied Mathematics  
New efficient algorithms for solving infinite-duration two-person adversary games with the decision problem in NP ∩ coNP, based on linear programming (LP), LP-representations, combinatorial LP, linear  ...  efficient algorithms in P-matrix linear complementarity theory.  ...  Acknowledgments Most ideas presented in this paper result from numerous discussions we had with Leonid since his visit to the Max-Planck Institut für Informatik, Saarbücken, in summer 1998, and during  ... 
doi:10.1016/j.dam.2008.04.012 fatcat:5fmgypimu5cs3ahclgd4lsc4si
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