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What about Linear Logic in Computer Science?

2013 Acta Polytechnica Hungarica  
We start with 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  ... 
doi:10.12700/aph.10.04.2013.4.9 fatcat:vk55sjgg2fgohcfbbglc6tbgva

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  ... 

Logical Time and Space of the Network Intrusion

Daniel Mihalyi, Jan Perhac, Patrik Balint
2017 Studia Universitatis Babes-Bolyai: Series Informatica  
This paper deals with the behavior 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.  ... 
doi:10.24193/subbi.2017.2.03 fatcat:rfts6yv725gn5mn4lqnvhbquea

Between syntax and semantics of resource oriented logic for IDS behavior description

Ján Perháč, Daniel Mihályi, Valerie Novitzká
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.  ... 
doi:10.17512/jamcm.2016.2.12 fatcat:xi5nth2lnzf5xghbqwiyb7r3qe

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

Vladimir Rybakov
2014 arXiv   pre-print
However, we would like to look to it from 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.  ... 
arXiv:1405.0559v1 fatcat:owjxv4srevayhelkqeqsjlinz4

Hybrid Categorial Logics

1995 Logic Journal of the IGPL  
Recent work within Categorial Grammar has seen the development 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.  ... 
doi:10.1093/jigpal/3.2-3.343 fatcat:y7ikv2w3u5fnfpzakahsxl2uly

Resource modalities in tensor logic

Paul-André Melliès, Nicolas Tabareau
2010 Annals of Pure and Applied Logic  
This revised point 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 !  ... 
doi:10.1016/j.apal.2009.07.018 fatcat:4jqktwfiava3lhfi7ay47kj7lq


Sergei Artemov, Michael Mislove
2006 Theoretical Computer Science  
Geometrical semantics for 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.  ... 
doi:10.1016/j.tcs.2006.03.008 fatcat:ctf7saz42fakvbgxamdh4cajzi

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).  ... 

In Praise of Strategies [chapter]

Johan van Benthem
2012 Lecture Notes in Computer Science  
Basic 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.  ... 
doi:10.1007/978-3-642-29326-9_6 fatcat:3atr6272gbfzhel5of5pnj5swe

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

Norihiro Kamide
2006 Theoretical Computer Science  
K , and 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.  ... 
doi:10.1016/j.tcs.2005.10.043 fatcat:z2vgcw2ttbfg3pagchehpzbrli

Modalities for model checking (extended abstract)

E. Allen Emerson, Chin-Laung Lei
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.)  ... 
doi:10.1145/318593.318620 dblp:conf/popl/EmersonL85 fatcat:x6kty74qarhxfhzekz7ey5ypvi

Forthcoming Papers

2001 Journal of Logic and Computation  
We introduce an abstract algebraic structure -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.  ... 
doi:10.1093/logcom/11.5.755 fatcat:6sp2os6ulfhmfkfvxczfheyl4a

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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