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What about Linear Logic in Computer Science?

2013
*
Acta Polytechnica Hungarica
*

We start with

doi:10.12700/aph.10.04.2013.4.9
fatcat:vk55sjgg2fgohcfbbglc6tbgva
*a*short overview*of**linear**logic*with an emphasis on the special properties*of**linear*implication and exponential operators. ... In this paper we discuss several useful features*of**linear**logic*especially from the viewpoint*of*computing science. ... If we consider resources,*a*resource 1 is consumed after*linear*implication, i.e. it becomes*a**linear*negation 1 ; Table 1 1*Linear*exponentials dealing with resources Operator Resource*view**Modal*...##
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Page 2074 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

Since propositional

*modal**logic*can be*viewed*as*a*fragment*of*“nasty” first-order*logic*, what is the cru- cial difference? ...*A*derivation z in*linear**logic*can be reduced to*a*derivation z* in classical*logic*by replacing the special connectives*of**linear**logic*with their classical counterparts and deleting the*linear**modal*...##
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Logical Time and Space of the Network Intrusion

2017
*
Studia Universitatis Babes-Bolyai: Series Informatica
*

This paper deals with the behavior

doi:10.24193/subbi.2017.2.03
fatcat:rfts6yv725gn5mn4lqnvhbquea
*of*the network intrusion detection system during specific network intrusion. We formally describe this network intrusion by the*modal**linear**logic*formula. ... Based on this formula,*logical*space and*logical*time is expressed from the attacker, and the network environment point*of**view*in the usage*of*the Ludics theory. ... This work is*a*result*of*international cooperation under the CEEPUS network No.CIII-HU-0019-12-1617. ...##
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Between syntax and semantics of resource oriented logic for IDS behavior description

2016
*
Journal of Applied Mathematics and Computational Mechanics
*

*Linear*

*logic*appears as

*a*suitable

*logical*system for description

*of*dynamic properties

*of*various network activities in computer science. ... We extend this

*logic*with Aristotelian

*modalities*and we formulate their appropriate model. ...

*Modal*

*linear*

*logic*In this section we firstly introduce basic notions

*of*

*linear*

*logic*and

*modal*operators

*of*Aristotle's

*modal*

*logic*. ...

##
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A Note on Parameterised Knowledge Operations in Temporal Logic
[article]

2014
*
arXiv
*
pre-print

However, we would like to look to it from

arXiv:1405.0559v1
fatcat:owjxv4srevayhelkqeqsjlinz4
*a*bit another point*of**view*, our paper models knowledge in terms*of**linear*temporal*logic*with past. ... The study*of*knowledge*logical*operations is originated around 1962 by representation*of*knowledge and belief using*modalities*. Nowadays, it is very good established area. ... However we would like to consider an interpretation*of**logical*knowledge operations via parameterized temporal operations. We will need*a*technique from the*linear*temporal*logic*and*modal**logics*. ...##
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Hybrid Categorial Logics

1995
*
Logic Journal of the IGPL
*

Recent work within Categorial Grammar has seen the development

doi:10.1093/jigpal/3.2-3.343
fatcat:y7ikv2w3u5fnfpzakahsxl2uly
*of**a*number*of*multimodal systems, where di erent families*of*connectives coexist within*a*single categorial*logic*. ... Although we focus mostly on the*view*taken in Hepple 7], and its inspiration by earlier work involving structural*modalities*, the paper proceeds to*a*discussion*of*whether the two approaches are genuinely ... used by Benton et al. (1992) with*linear**logic*. ...##
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Resource modalities in tensor logic

2010
*
Annals of Pure and Applied Logic
*

This revised point

doi:10.1016/j.apal.2009.07.018
fatcat:4jqktwfiava3lhfi7ay47kj7lq
*of**view*leads us to introduce tensor*logic*,*a*primitive variant*of**linear**logic*where negation is not involutive. ... 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 ... Finally, the exponential*modality**of**linear**logic*! ...##
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Preface

2006
*
Theoretical Computer Science
*

Geometrical semantics for

doi:10.1016/j.tcs.2006.03.008
fatcat:ctf7saz42fakvbgxamdh4cajzi
*Linear**Logic*(Multiplicative Fragment), by Sergey Slavnov.*Linear**Logic*LL was introduced by J.-Y. Girard as*a**logic**of*dynamic interactions. ... From this point*of**view*, proofs in*Linear**Logic*are interpreted as (geometric approximations to) quantum states and formulas as specifications for these states. ...##
###
Page 3572 of Mathematical Reviews Vol. , Issue 2001F
[page]

2001
*
Mathematical Reviews
*

*Viewing*first-order

*logic*as

*a*product

*of*

*modal*

*logics*, we derive

*a*strong counterexample for failure

*of*interpolation in the finite variable fragments

*of*first-order

*logic*. ... The paper gives

*a*short overview

*of*

*a*novel approach to

*linear*

*logic*and proof-nets, based on the 2-sequents

*of*

*A*. Masini (1992). ...

##
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In Praise of Strategies
[chapter]

2012
*
Lecture Notes in Computer Science
*

Basic

doi:10.1007/978-3-642-29326-9_6
fatcat:3atr6272gbfzhel5of5pnj5swe
*modal**logic*Extensive game trees may be*viewed*as state spaces for some multi-agent process. ... This operation takes us outside*of*PDL proper, but then, PDL « with intersections added is still*a*reasonably simple*modal*language. Stronger*modal**logics**of*strategies? ... Thus, propositional dynamic*logic*does*a*reasonable job in defining explicit strategies in simple extensive games. ...##
###
Page 4934 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

*A*first-order temporal

*logic*based on

*a*

*linear*discrete model structure is introduced and the procedure for transform- ing an arbitrary formula

*of*this

*logic*to SNF; is described. ... to

*logic*. (3) His use

*of*tense

*logic*in metaphysics. (4) His

*view*on the relation between tense

*logic*and natural science in general. (5) The conflict between the tensed

*view*

*of*time and the special theory ...

##
###
Linear and affine logics with temporal, spatial and epistemic operators

2006
*
Theoretical Computer Science
*

K , and

doi:10.1016/j.tcs.2005.10.043
fatcat:z2vgcw2ttbfg3pagchehpzbrli
*a**linear**modal*operator ! ...*A*temporal spatial epistemic intuitionistic*linear**logic*(TSEILL) is introduced, and the completeness theorem for this*logic*is proved with respect to Kripke semantics. ... Conclusions In this paper,*a*number*of*combined multi-*modal**logics*based on the resource-sensitive*logics*were studied from*a*purely*logical*point*of**view*. ...##
###
Modalities for model checking (extended abstract)

1985
*
Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '85
*

*modalities*

*of*my branching time

*logic*? ... (Remark: In

*a*basic

*modality*

*of*

*a*branching time

*logic*, the

*linear*time formula following the path quantifier is

*a*Upure "

*linear*time formula involving no nested path quantifiers.) ...

##
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Forthcoming Papers

2001
*
Journal of Logic and Computation
*

We introduce an abstract algebraic structure -

doi:10.1093/logcom/11.5.755
fatcat:6sp2os6ulfhmfkfvxczfheyl4a
*a*lattice defined on*a*generalized truth value space*of*constructive*logic*. ... For background one can refer to the idea*of*"under-determined" and "over-determined" valuations (Dunn),*a*"useful four-valued*logic*" (Belnap), and the notion*of**a*bilattice (Ginsberg). ... Demri*A**modal*reduction principle*of*the form ½ Ò Ô µ ½ Ò ¼ Ô can be*viewed*as*a*production rule ½ ¡ ¡ Ò ½ ¡ ¡ Ò ¼ in*a*formal grammar. ...##
###
Page 2327 of Mathematical Reviews Vol. , Issue 2002D
[page]

2002
*
Mathematical Reviews
*

Summary: “

*Logic*, in particular*modal**logic*, can be used not only in semantics but also in syntax. Here we study syntactic formalisms from*a**logical*point*of**view*. ... This is*a*reflection in terms*of**logic**of*the*view*that grammar is nothing but*a*catalogue*of*abstract descriptive principles rather than*a*productive device,*a**view*that was current mainly in the 1980s ...
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