Filters








331,717 Hits in 3.4 sec

Operational interpretations of linear logic

David N. Turner, Philip Wadler
1999 Theoretical Computer Science  
Moreover, we show that there is a subset of linear logic where the two operational interpretations coincide.  ...  Two di erent operational interpretations of intuitionistic linear logic have been proposed in the literature. The simplest interpretation recomputes non-linear values every time they are required.  ...  Introduction Two di erent operational interpretations of linear logic have been proposed in the literature. The two interpretations di er primarily in their treatment of non-linear values.  ... 
doi:10.1016/s0304-3975(99)00054-7 fatcat:eglmzi4gkzhx7itc655phn3phq

A categorical model of predicate linear logic

Emilia Demeterova, Daniel Mihalyi, Valerie Novitzka
2015 Journal of Applied Mathematics and Computational Mechanics  
Linear logic is one of the logical systems with special properties suitable for describing real processes used in computer science.  ...  Mainly, propositional linear logic is used for these purposes. The expression power of linear logic significantly grows by extending propositional logic with predicates and quantifiers.  ...  Acknowledgment This work has been supported by APVV-0008 0 Grant: Modelling, simulation and implementation of GPGPU-enabled architectures of high-throughput network security tools.  ... 
doi:10.17512/jamcm.2015.1.03 fatcat:mf47nb4mpjd6jcpedkjelp5pje

An infinitary model of linear logic [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets.  ...  We explain how to interpret in this model the fixpoint operator Y as a Conway operator alternatively defined in an inductive or a coinductive way.  ...  Fixpoint operators in models of linear logic We want to extend linear logic with a fixpoint rule: ! X⊗ ! A ⊢ A f ix !  ... 
arXiv:1411.4380v3 fatcat:lxj4n52rqbardkoji5747wv3c4

Combining abstract interpreters

Sumit Gulwani, Ashish Tiwari
2006 Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation - PLDI '06  
This lends modularity to the process of design and implementation of abstract interpreters. We define the notion of logical product of lattices.  ...  We prove that our combination methodology yields the most precise abstract interpretation operators over the logical product of lattices when the individual lattices are over theories that are convex,  ...  Acknowledgments We thank the anonymous reviewers of this paper for their useful and insightful comments.  ... 
doi:10.1145/1133981.1134026 dblp:conf/pldi/GulwaniT06 fatcat:y5zkvl77dfasxosmfz4hucjjva

Combining abstract interpreters

Sumit Gulwani, Ashish Tiwari
2006 SIGPLAN notices  
This lends modularity to the process of design and implementation of abstract interpreters. We define the notion of logical product of lattices.  ...  We prove that our combination methodology yields the most precise abstract interpretation operators over the logical product of lattices when the individual lattices are over theories that are convex,  ...  Acknowledgments We thank the anonymous reviewers of this paper for their useful and insightful comments.  ... 
doi:10.1145/1133255.1134026 fatcat:grdxypzkbncwtk2djze4feo23a

Page 2373 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
, and describes a game interpretation of this linear logic and the affine logic which is the extension of LL with the rule of weakening.  ...  Beginning with definitions of games and operations on connectives that correspond to those of linear logic, the author presents a formal system which differs from Girard’s linear logic only in notations  ... 

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.  ...  We consider various versions of logical knowledge operations which may be defined in this framework.  ...  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

Uncertain Linear Logic via Fibring of Probabilistic and Fuzzy Logic [article]

Ben Goertzel
2020 arXiv   pre-print
It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic.  ...  The concept of linear logic as a "logic of resources" is manifested here via the principle of "conservation of evidence" -- the restrictions to weakening and contraction in linear logic serve to avoid  ...  Or, stated more concretely in terms of the connectives of linear logic: !a =!a ⊗ a. In our evidential linear logic, !a can be interpreted to mean an infinite amount of evidence about A.  ... 
arXiv:2009.12990v1 fatcat:xamscskdsreszgi5qp2jxzvgda

Petri nets as models of linear logic [chapter]

Uffe Engberg, Glynn Winskel
1990 Lecture Notes in Computer Science  
To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic.  ...  The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes.  ...  The logical operation, ⊗, is interpreted by the corresponding binary operation in the quantale and the logical constant 1 is interpreted as 1 in the quantale.  ... 
doi:10.1007/3-540-52590-4_46 fatcat:kuxykwwll5gv7nts7ijv2efkmu

Petri Nets as Models of Linear Logic

Uffe Engberg, Glynn Winskel
1990 DAIMI Report Series  
To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic.  ...  The chief purpose of this paper is to appraise the feasibility of Girad's linear logic as a specification language for parallel processes.  ...  The logical operation, ⊗, is interpreted by the corresponding binary operation in the quantale and the logical constant 1 is interpreted as 1 in the quantale.  ... 
doi:10.7146/dpb.v19i301.6682 fatcat:kk3sqzejtvhyrlclxsdnxeyvxi

Concurrent systems analysis using ECATNets

F Belala
2000 Logic Journal of the IGPL  
The categorical interpretation of the extra structure is inspired from that of some linear logic connectors.  ...  The definition of this extra structure is inspired from the categorical interpretation of some linear logic connectors.  ...  The general idea is to enrich the ECATNet rewrite theory with the definition of some operations whose interpretation is similar to that of linear logical connectors: &,´, ⊕, ∂.  ... 
doi:10.1093/jigpal/8.2.149 fatcat:xm5cgj6gnfct7gnfqxddkwv6mm

Relating State-Based and Process-Based Concurrency through Linear Logic

Iliano Cervesato, Andre Scedrov
2006 Electronical Notes in Theoretical Computer Science  
In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic.  ...  The resulting interpretation is extended with a majority of linear connectives into the language of ω-multisets.  ...  Acknowledgments We are grateful to Frank Pfenning, Dale Miller, Mark-Oliver Stehr, Valeria de Paiva, Gerald Allwein, Steve Zdancevic and Vijay Saraswat for their comments on various aspects of this work  ... 
doi:10.1016/j.entcs.2006.05.043 fatcat:eavrmrbudjbvbhnu2zlxecsd2e

Linear Non-Transitive Temporal Logic, Knowledge Operations, Algorithms for Admissibility [article]

Vladimir Rybakov
2014 arXiv   pre-print
The paper studies problems of satisfiability, decidability and admissibility of inference rules, conceptions of knowledge and agent's knowledge in non-transitive temporal linear logic LTL(Past,m).  ...  We discuss several ways to formalize conceptions of knowledge and agent's knowledge within given approach in non-transitive linear logic with models directed to past.  ...  Earlier logical knowledge operations (agents knowledge) were just unary logical operations K i interpreted as S5modalities, and knowledge operations were introduced via the vote of agents about truth the  ... 
arXiv:1406.2783v1 fatcat:6cfec3emmbao3kvmnvlrrc7gga

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  , and a set of temporal operators defined for each logic.  ...  It is one of the most expressive propositional interval logic over linear orderings [68] . CDT includes the binary modal operators C, D and T .  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

A survey on temporal logics for specifying and verifying real-time systems

Savas Konur
2013 Frontiers of Computer Science  
In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time  ...  Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature.  ...  Some parts of this paper exists in [231] .  ... 
doi:10.1007/s11704-013-2195-2 fatcat:5lyaji5wnzbyfdmbxwzbxjosku
« Previous Showing results 1 — 15 out of 331,717 results