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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

doi:10.1016/j.entcs.2011.03.009
fatcat:wyzvjdecyvaebolnebwgliih6i
*proof**systems*by using focused*linear**logic**with**subexponentials*. ...*In*the past years,*linear**logic*has been successfully used as a general*logical*framework for encoding*proof**systems*. ... This*subexponential*is used to store*linear**logic*theories*specifying**proof**systems*. ...##
###
An extended framework for specifying and reasoning about proof systems

2014
*
Journal of Logic and Computation
*

First,

doi:10.1093/logcom/exu029
fatcat:uontgaw6gbfh3mcyxzpgdc7jqu
*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*. ... Section 2 introduces the*proof**system*for*linear**logic**with**subexponentials*, called SELLF, which is the basis of the proposed*logical*framework. ... We are also grateful to Kaustuv Chaudhuri for pointing out an error*in*a previous version of this paper. ...##
###
Quati: An Automated Tool for Proving Permutation Lemmas
[chapter]

2014
*
Lecture Notes in Computer Science
*

Given a

doi:10.1007/978-3-319-08587-6_18
fatcat:ym2kxrefqrgylh7agegchqrgvy
*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*. ...##
###
(Mathematical) Logic for Systems Biology (Invited Paper)
[chapter]

2016
*
Lecture Notes in Computer Science
*

We present two candidate

doi:10.1007/978-3-319-45177-0_1
fatcat:imfgsz4r4jdfdi5et7jkrw7gwy
*logics*(two modal extensions of*linear**logic*, called HyLL and SELL), along*with*biological examples. ... The examples we have considered so far are very simple ones-coming*with*completely formal (interactive)*proofs**in*Coq. ... For instance,*subexponentials*can be used to represent contexts of*proof**systems*[16] ; to*specify**systems**with*temporal, epistemic and spatial modalities [18] and to*specify*and verify biological*systems*...##
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A Logical Framework with Commutative and Non-commutative Subexponentials
[chapter]

2018
*
Lecture Notes in Computer Science
*

Motivated by applications

doi:10.1007/978-3-319-94205-6_16
fatcat:lscl6zdtvfc33oxrsu43unsudm
*in*distributed*systems*and*in*type-*logical*grammar, we propose a*linear**logical*framework containing both commutative and non-commutative*subexponentials*. ...*Linear**logical*frameworks have been successfully used for the specification of a number of computational,*logics*and*proof**systems*. ...*In*our previous work [10] , we proposed the*proof**system*SNILL Σ (*Subexponential*Non-Commutative Intuitionistic*Linear**Logic*) 7 which extends propositional Lambek Calculus*with**subexponentials*. ...##
###
Hybrid and Subexponential Linear Logics

2017
*
Electronical Notes in Theoretical Computer Science
*

HyLL (Hybrid

doi:10.1016/j.entcs.2017.04.007
fatcat:ov52p5wcmjcurlpnlcuznebccm
*Linear**Logic*) and SELL (*Subexponential**Linear**Logic*) are*logical*frameworks that have been extensively used for*specifying**systems*that exhibit modalities such as temporal or spatial ones. ... Both frameworks have*linear**logic*(LL) as a common ground and they admit (cut-free) complete focused*proof**systems*. The difference relies on the way modalities are handled. ...*Subexponentials**in**Linear**Logic**Linear**logic**with**subexponentials*4 (SELL) shares*with*LL all its connectives except the exponentials: instead of having a single pair of exponentials ! and ? ...##
###
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*. ... The

*linear*

*logic*exponentials !, ? are not canonical: one can add to

*linear*

*logic*other such operators, say ! l , ? ... 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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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. ... LALs have been used

*in*the context of the

*Proof*-Carrying Authorization framework, where formal

*proofs*must be constructed

*in*order for a principal to gain access to some resource elsewhere. ... We now review the

*proof*

*system*for intuitionistic

*linear*

*logic*

*with*

*subexponentials*

*in*Section 2.1 and the focused

*proof*

*system*for this

*system*, called SELLF,

*in*Section 2.2. ...

##
###
A Proof Theoretic Study of Soft Concurrent Constraint Programming

2014
*
Theory and Practice of Logic Programming
*

*In*this work, we give a

*proof*theoretical meaning to soft constraints: they can be defined as formulas

*in*a suitable fragment of ILL

*with*

*subexponentials*(SELL) where

*subexponentials*, ordered

*in*a c-semiring ...

*In*fact, the underlying constraint

*system*can be built from a suitable fragment of intuitionistic (

*linear*)

*logic*-ILL- and processes can be interpreted as formulas

*in*ILL. ...

*In*Section 3, we will

*specify*such

*systems*as formulas

*in*intuitionistic

*linear*

*logic*(ILL (Girard 1987) ). ...

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

2021
*
Electronic Proceedings in Theoretical Computer Science
*

This is called the meta-theory of a

doi:10.4204/eptcs.337.1
fatcat:dobvkljpbraxfgyc5qtbdwoufq
*proof**system*. Meta-theory*proofs*typically involve many cases on structures*with*lots of symbols. ... For this to be possible,*proof**systems*must be designed as a set of rules such that*proofs*using those rules are correct by construction. ... It turns out that the*linear**logic*framework cannot capture so easily sequent calculus*systems**with*rules that have side conditions*in*the context, such as: Γ A Γ, Γ A, ∆ R To be able to*specify*rules ...##
###
Subexponential concurrent constraint programming

2015
*
Theoretical Computer Science
*

*In*previous works we have shown that

*linear*

*logic*

*with*

*subexponentials*(SELL), a refinement of

*linear*

*logic*, can be used to

*specify*emergent features of concurrent constraint programming (CCP) languages ...

*In*order to provide the

*proof*theoretic foundations for such a language, we propose a unified

*logical*framework (SELLS ) combining the extensions of

*linear*

*logic*

*with*

*subexponentials*mentioned above, and ... We believe that

*linear*

*logic*together

*with*the strong levels of adequacy may help us develop more general techniques for verifying CCP programs. ...

##
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Hybrid and Subexponential Linear Logics Technical Report
[article]

2016
*
arXiv
*
pre-print

HyLL (Hybrid

arXiv:1608.08779v2
fatcat:pqnhffzanfamlgwix2ncdmdroa
*Linear**Logic*) and SELL (*Subexponential**Linear**Logic*) are*logical*frameworks that have been extensively used for*specifying**systems*that exhibit modalities such as temporal or spatial ones. ... Both frameworks have*linear**logic*(LL) as a common ground and they admit (cut-free) complete focused*proof**systems*. The difference between the two*logics*relies on the way modalities are handled. ... L] Hybrid connectives Figure 5 : Focused*linear**logic**system**with*(quantified)*subexponentials*. ...##
###
Hybrid linear logic, revisited

2019
*
Mathematical Structures in Computer Science
*

Another extension of LL that has extensively been used for

doi:10.1017/s0960129518000439
fatcat:ovn75fwk4rfq3pmuybe4luwrtm
*specifying**systems**with*modalities is*Subexponential**Linear**Logic*(SELL).*In*SELL, the LL exponentials (!, ?) ... HyLL (Hybrid*Linear**Logic*) is an extension of intuitionistic*linear**logic*(ILL) that has been used as a framework for*specifying**systems*that exhibit certain modalities. ...*logic**system**with*(quantified)*subexponentials*. ...##
###
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. ... LAL has been used

*in*the context of the

*Proof*-Carrying Authorization framework, where formal

*proofs*are constructed

*in*order for a principal to gain access to some resource elsewhere. ... We now review the

*proof*

*system*for intuitionistic

*linear*

*logic*

*with*

*subexponentials*. ...

##
###
A proof theoretic view of spatial and temporal dependencies in biochemical systems

2016
*
Theoretical Computer Science
*

To this aim, we consider a fragment of intuitionistic

doi:10.1016/j.tcs.2016.03.029
fatcat:t3t2p7qy5fgunda44sog6slufi
*linear**logic**with**subexponentials*(SELL). ...*In*this paper we propose a formalism for*specifying*and verifying properties of biochemical*systems*that combines, coherently, temporal and spatial modalities. ...*Linear**logic**with**subexponentials**In*this section we recall the*proof*theory of intuitionistic*linear**logic*(ILL) [6]*with**subexponentials*[7, 8] . ...
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