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Algorithmic specifications in linear logic with subexponentials

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. ...

##
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Specifying Proof Systems in Linear Logic with Subexponentials

2011
*
Electronical Notes in Theoretical Computer Science
*

This work shows that one can encode a wider range of proof systems by using focused

doi:10.1016/j.entcs.2011.03.009
fatcat:wyzvjdecyvaebolnebwgliih6i
*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*. ...##
###
Quati: An Automated Tool for Proving Permutation Lemmas
[chapter]

2014
*
Lecture Notes in Computer Science
*

Given a proof system

doi:10.1007/978-3-319-08587-6_18
fatcat:ym2kxrefqrgylh7agegchqrgvy
*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*. ...##
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Subexponentials in non-commutative linear logic
[article]

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*. ...

##
###
Facilitating Meta-Theory Reasoning (Invited Paper)

2021
*
Electronic Proceedings in Theoretical Computer Science
*

Meta-theory proofs typically involve many cases on structures

doi:10.4204/eptcs.337.1
fatcat:dobvkljpbraxfgyc5qtbdwoufq
*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. ...##
###
Soft Subexponentials and Multiplexing
[chapter]

2020
*
Lecture Notes in Computer Science
*

One of the

doi:10.1007/978-3-030-51074-9_29
fatcat:rx3qbmznpzdh7fme4xiv27bqgu
*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] . ...##
###
Classical and Intuitionistic Subexponential Logics are Equally Expressive
[article]

2010
*
arXiv
*
pre-print

It is standard to regard the intuitionistic restriction of a classical

arXiv:1006.3134v1
fatcat:mlzrr7v4ajb7nm5h2nfpbhnswi
*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 ...##
###
Classical and Intuitionistic Subexponential Logics Are Equally Expressive
[chapter]

2010
*
Lecture Notes in Computer Science
*

It is standard to regard the intuitionistic restriction of a classical

doi:10.1007/978-3-642-15205-4_17
fatcat:2wu4xiliovdatgokl2mb6abzva
*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 ...##
###
An extended framework for specifying and reasoning about proof systems

2014
*
Journal of Logic and Computation
*

Finally, we have implemented a tool, described

doi:10.1093/logcom/exu029
fatcat:uontgaw6gbfh3mcyxzpgdc7jqu
*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. ...##
###
An Adequate Compositional Encoding of Bigraph Structure in Linear Logic with Subexponentials
[chapter]

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 ...

##
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Verification of Spatial and Temporal Modalities in Biochemical Systems

2015
*
Electronical Notes in Theoretical Computer Science
*

For that, we use as

doi:10.1016/j.entcs.2015.06.009
fatcat:ksphyjbd5fbqheyjhhoiyoy72a
*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 ?. ...##
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A framework for linear authorization logics

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. ...

##
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On the Complexity of Linear Authorization Logics

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] . ...

##
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Combinatorial structure and randomized subexponential algorithms for infinite games

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. ...

##
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Cyclic games and linear programming

2008
*
Discrete Applied Mathematics
*

New efficient

doi:10.1016/j.dam.2008.04.012
fatcat:5fmgypimu5cs3ahclgd4lsc4si
*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 ...
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