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An Explicit Formula for the Free Exponential Modality of Linear Logic
[chapter]

2009
*
Lecture Notes in Computer Science
*

*The*

*exponential*

*modality*

*of*

*linear*

*logic*associates a commutative comonoid !A to every

*formula*A in order to duplicate it. Here, we explain how to compute

*the*

*free*commutative comonoid ! ... This algebraic approach enables to unify

*for*

*the*rst time apparently dierent constructions

*of*

*the*

*exponential*

*modality*in spaces and games. ...

*The*authors would like to thank Thomas Ehrhard and Martin Hyland

*for*enlightening discussions and feedbacks. ...

##
###
An explicit formula for the free exponential modality of linear logic

2017
*
Mathematical Structures in Computer Science
*

*The*

*exponential*

*modality*

*of*

*linear*

*logic*associates to every

*formula*A a commutative comonoid !A which can be duplicated in

*the*course

*of*reasoning. ... This algebraic description unifies

*for*

*the*first time a number

*of*apparently different constructions

*of*

*the*

*exponential*

*modality*in spaces and games. ...

*The*authors would like to thank Thomas Ehrhard and Martin Hyland

*for*enlightening discussions and feedbacks. ...

##
###
An analysis of (linear) exponentials based on extended sequents

1998
*
Logic Journal of the IGPL
*

We apply

doi:10.1093/jigpal/6.5.735
fatcat:vkd5mqlgtfbqvaw7whpk72zzba
*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-sequence is*an*expression 0 1 . . . n in which each i is*an*ordinary (possibly empty) sequence*of**linear**formulas*.*The**formulas**of*i are at level i. ...##
###
Decision Problems for Second-Order Linear Logic
[chapter]

1997
*
Logic and Scientific Methods
*

*The*decision problem is studied

*for*fragments

*of*second-order

*linear*

*logic*without

*modalities*. ... Among

*the*consequences are

*the*undecidability

*of*

*the*intuitionistic second-order fragment

*of*propositional multiplicative

*linear*

*logic*and

*the*undecidability

*of*multiplicative

*linear*

*logic*with rst-order ...

*The*decidability

*of*mell,

*the*fragment

*of*quanti er-

*free*propositional

*logic*that contains multiplicatives and

*exponentials*(

*modalities*) but not additives, remains

*an*interesting open problem. ...

##
###
From linear proofs to direct logic with exponentials
[chapter]

1997
*
Lecture Notes in Computer Science
*

Following

doi:10.1007/3540634932_10
fatcat:fi62ng247fgghmcygtnfa6tgly
*the*idea*of**Linear*Proofs presented in 4] we introduce*the*Direct*Logic*14] with*exponentials*(DLE).*The**logic*combines Direct*Logic*with*the**exponentials**of**Linear**Logic*. ...*For*a well-chosen subclass*of**formulas**of*this*logic*we provide a matrix-characterization which can be used as a foundation*for*proof-search methods based on*the*connection calculus. ... Herbrand theorem*for*Direct*Logic*. Let 2 F nnf be*an**exponential*and universal quanti er*free*sentence. ...##
###
Resource modalities in tensor logic

2010
*
Annals of Pure and Applied Logic
*

*The*description

*of*resources in game semantics has never achieved

*the*simplicity and precision

*of*

*linear*

*logic*, because

*of*

*the*misleading conception that

*linear*

*logic*is more primitive than game semantics ...

*linear*, affine, relevant or

*exponential*. ... Acknowledgement This work is supported by

*the*ANR Curry-Howard Correspondence and Concurrency Theory (CHOCO). ...

##
###
Page 8788 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

As a corollary, it is shown that a

*linear*Kripke models which satisfies*the*principle*of*excluded middle*for**formulas*in prenex normal form also satisfies*the*principle*of*excluded middle*for*all*formulas*...*The*other result is a characterization*of*those*linear*Kripke structures which decide all Ao-*formulas*, and in which forcing and satisfaction*for*Il,,*formulas*coincide. ...##
###
Logic of predicates with explicit substitutions
[chapter]

1996
*
Lecture Notes in Computer Science
*

We present a non-commutative

doi:10.1007/3-540-61550-4_148
fatcat:7srloqu57vdvzhn3qcllmwck2y
*linear**logic*|*the**logic**of*predicates with equality and*explicit*substitutions. ...*Linear**logic*is not*an*alternative*logic*; it should rather be seen as*an*extension*of*usual*logic*. This paper aims at supporting*the*same idea. ...*The*research presented here was partially sponsored by*The*State Committee*for*Scienti c Research, Grant No 2P301 007 04. ...##
###
Substructural logics on display

1998
*
Logic Journal of the IGPL
*

from tense

doi:10.1093/jigpal/6.3.451
fatcat:erqlhxit7fe25a4gmybgimeuzy
*logic*,*the**exponentials**of**linear**logic*,*the*converse operator familiar from relation algebra, four negations, and two unusual*modalities*corresponding to*the*non-classical analogues*of*Sheffer's ...*The*addition*of**the*structural rules then gives Bi-*linear*, Bi-relevant, Bi-BCK and Bi-intuitionistic*logic*, again in*an*incremental way. ...*logical**modalities*, quite at odds with*the*usual*exponentials**of**linear**logic*. ...##
###
Correctness and Worst-Case Optimality of Pratt-Style Decision Procedures for Modal and Hybrid Logics
[chapter]

2011
*
Lecture Notes in Computer Science
*

Our development is modular and we extend it stepwise from

doi:10.1007/978-3-642-22119-4_16
fatcat:a3et5obo7zazbm3v2u5435lgue
*modal**logic*with eventualities to*the*full*logic*. ⋆ This is*an*author version*of**the*contribution to Proc. TABLEAUX 2011. ...*The*main theorem states that a*formula*is satisfiable if and only if it is contained in a demo. From this theorem*the*correctness*of**the*decision procedure is easily obtained. ... We thank*the*anonymous reviewers*for*helpful comments. References ...##
###
Finite Model Reasoning in Expressive Fragments of First-Order Logic

2017
*
Electronic Proceedings in Theoretical Computer Science
*

*the*image

*of*

*the*standard translation

*of*

*modal*

*logic*to first-order

*logic*. ... When presenting

*the*material special attention is given to decision procedures

*for*

*the*finite satisfiability problems, as many

*of*

*the*fragments discussed contain infinity axioms. ... In fact in [50]

*an*

*exponential*reduction from UNFP to

*the*

*modal*µ-calculus is presented that additionally preserves finiteness

*of*

*the*models. ...

##
###
Beth Definability for the Guarded Fragment
[chapter]

1999
*
Lecture Notes in Computer Science
*

*The*Beth property

*for*GF is here established on

*the*basis

*of*a limited form

*of*interpolation, which more closely resembles

*the*interpolation property that is usually studied in

*modal*

*logics*. ...

*The*guarded fragment (GF) was introduced in [1] as a fragment

*of*first order

*logic*which combines a great expressive power with nice

*modal*behavior. ...

*The*same

*for*

*explicit*definitions. Description

*Logics*Description

*logics*were designed

*for*

*the*purpose

*of*knowledge representation. ...

##
###
Symbolic Model Checking of Non-regular Properties
[chapter]

2004
*
Lecture Notes in Computer Science
*

This paper presents a symbolic model checking algorithm

doi:10.1007/978-3-540-27813-9_7
fatcat:gizk33jb3jghdndfjrebkx25iu
*for*Fixpoint*Logic*with Chop,*an*extension*of**the**modal*µ-calculus capable*of*defining non-regular properties. ... Some empirical data about running times*of*a naive implementation*of*this algorithm are given as well. ... Acknowledgments We would like to thank*the*anonymous referee who suggested*the*variable ordering used in this version. It hugely improved*the*performance compared to*the*previous version. ...##
###
Preface

2016
*
Mathematical Structures in Computer Science
*

*An*obvious remark is that LL yielded a first

*logical*quantitative account

*of*

*the*use

*of*resources:

*the*

*logical*distinction between

*linear*and non-

*linear*

*formulas*through

*the*introduction

*of*

*the*

*exponential*...

*Linear*

*Logic*(DiLL) and

*the*differential λ-calculus. ...

*The*last paper

*of*

*the*volume, '

*An*

*explicit*

*formula*

*for*

*the*

*free*

*exponential*

*modality*

*of*LL by Paul-André Melliès, Nicolas Tabareau and Christine Tasson, attacks

*the*general question

*of*

*the*categorical ...

##
###
Reasoning with Global Assumptions in Arithmetic Modal Logics
[chapter]

2015
*
Lecture Notes in Computer Science
*

Unlike earlier results

doi:10.1007/978-3-319-22177-9_28
fatcat:ggkvnu5drjahtp4cdtwq24x7hu
*of*this kind, we do not require a tractable set*of*tableau rules*for**the*instance*logics*, so that*the*result applies to wider classes*of**logics*. ... Examples are Presburger*modal**logic*, which extends graded*modal**logic*with*linear*inequalities over numbers*of*successors, and probabilistic*modal**logic*with polynomial inequalities over probabilities. ... Catesbeiana*for*remarks on unsatisfiability. Work*of**the*first author forms part*of**the*DFG project GenMod2 (SCHR 1118/5-2). ...
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