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Subexponential concurrent constraint programming

Carlos Olarte, Elaine Pimentel, Vivek Nigam
2015 Theoretical Computer Science  
In order to do so, we introduced a number of extensions to SELL, such as subexponential quantifiers for the specification of modalities, and more elaborated subexponential structures for the specification  ...  showing that this new framework has interesting proof theoretical properties such as cut-elimination and a sound and complete focused proof system.  ...  We are currently investigating methods for verifying systems specified in Mccp which mention spatial properties, e.g., the Airport Security problem [39] .  ... 
doi:10.1016/j.tcs.2015.06.031 fatcat:otxe47mfjnf75i4nov2yn7ifya

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

C. Olarte, D. Chiarugi, M. Falaschi, D. Hermith
2016 Theoretical Computer Science  
In this paper we propose a formalism for specifying and verifying properties of biochemical systems that combines, coherently, temporal and spatial modalities.  ...  The behavior of biochemical systems such as metabolic and signaling pathways may depend on either the location of the reactants or on the time needed for a reaction to occur.  ...  Acknowledgements We thank the anonymous reviewers for their detailed comments and suggestions which helped us to improve our paper.  ... 
doi:10.1016/j.tcs.2016.03.029 fatcat:t3t2p7qy5fgunda44sog6slufi

Verification of Spatial and Temporal Modalities in Biochemical Systems

Davide Chiarugi, Moreno Falaschi, Diana Hermith, Carlos Olarte
2015 Electronical Notes in Theoretical Computer Science  
We address the problem of specifying and verifying properties of biochemical systems that exhibit both temporal and spatial modalities at the same time.  ...  Biochemical systems such as metabolic and signaling pathways tend to be arranged in a physical space: the product of one reaction must be in the right place to become the reactant for the subsequent reaction  ...  In order to combine spatial and temporal modalities in SELL we need first to define a subexponential signature as the one depicted in Figure 2 .  ... 
doi:10.1016/j.entcs.2015.06.009 fatcat:ksphyjbd5fbqheyjhhoiyoy72a

A Proof Theoretic Study of Soft Concurrent Constraint Programming

2014 Theory and Practice of Logic Programming  
An interesting side effect of (1) is that one is also able to handle probabilities (and other modalities) in SELL, by restricting the use of the promotion rule for non-idempotent c-semirings.This finer  ...  way of controlling subexponentials allows for considering more interesting spaces and restrictions, and it opens the possibility of specifying more challenging computational systems.  ...  Nigam was supported by CNPq and Pimentel was supported by CNPq and CAPES.  ... 
doi:10.1017/s147106841400026x fatcat:z5cdsnb3hbd6jmmjqzrfhyneai

(Mathematical) Logic for Systems Biology (Invited Paper) [chapter]

Joëlle Despeyroux
2016 Lecture Notes in Computer Science  
This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience.  ...  The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq.  ...  In these first experiments, we focused on Boolean systems and in this case a time unit corresponds to a transition in the system.  ... 
doi:10.1007/978-3-319-45177-0_1 fatcat:imfgsz4r4jdfdi5et7jkrw7gwy

Dynamic Spaces in Concurrent Constraint Programming

Carlos Olarte, Vivek Nigam, Elaine Pimentel
2014 Electronical Notes in Theoretical Computer Science  
Concurrent constraint programming (CCP) is a declarative model for concurrency where agents interact with each other by posting and asking constraints (formulas in logic) in a shared store of partial information  ...  This strategy has been used, for instance, to model the generation and communication of fresh values (nonces) in mobile reactive systems as security protocols; and (2) the underlying constraint system  ...  This work has been (partially) supported by Colciencias (Colombia), and by Digiteo and DGAR (École Polytechnique) funds for visitors.  ... 
doi:10.1016/j.entcs.2014.06.008 fatcat:wuok733tqzfrlk3ptymgyyqppy

A framework for linear authorization logics

Vivek Nigam
2014 Theoretical Computer Science  
Finally, we argue by example that the latter fragment is natural and can be used in practice.  ...  On the other hand, we also identify a first-order fragment of LAL for which provability is PSPACE-complete.  ...  Finally, we also thank the anonymous reviewers for their detailed comments on a previous version of this paper. Nigam was supported by the CNPq.  ... 
doi:10.1016/j.tcs.2014.02.018 fatcat:22pxpnai5vflfhhq6sv6wmwvbi

Algorithmic specifications in linear logic with subexponentials

Vivek Nigam, Dale Miller
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
We also give some general conditions for when a focused proof step can be executed in constant time.  ...  are not canonical: one can add to linear logic other such operators, say ! l , ? l , which may or may not allow contraction and weakening, and where l is from some pre-ordered set of labels.  ...  Focused proofs with Subexponentials In [1] , Andreoli presented a focused proof system for linear logic: similar focused proof systems have subsequently been introduced for classical and intuitionistic  ... 
doi:10.1145/1599410.1599427 dblp:conf/ppdp/NigamM09 fatcat:2xzv7s5wlzh4polnubupd6divq

Expressing additives using multiplicatives and subexponentials

2016 Mathematical Structures in Computer Science  
We then show how the additive connectives can be directly simulated by giving an encoding of propositional multiplicative additive linear logic (MALL) in an MSEL with one unrestricted and four linear subexponentials  ...  Subexponential logic is a variant of linear logic with a family of exponential connectives – called subexponentials – that are indexed and arranged in a pre-order.  ...  Acknowledgements We thank Giselle Reis for many fruitful discussions about encoding proof systems in SEL, and Anupam Das for his encouragement to finish the material in Section 5.  ... 
doi:10.1017/s0960129516000293 fatcat:lgl2vrbnczby7ez2w72slx3quq

Subexponentials in non-commutative linear logic [article]

Max Kanovich, Stepan Kuznetsov, Vivek Nigam, Andre Scedrov
2017 arXiv   pre-print
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics.  ...  This paper investigates the proof theory of linear logic proof systems in the non-commutative variant. These systems can disallow the application of exchange rule on some subexponentials.  ...  While their focused proof system contained a single unbounded, a single bounded and a single non-commutative modalities, focused proof systems with commutative and non-commutative subexponentials would  ... 
arXiv:1709.03607v1 fatcat:ft5zuquzsza25a3csdz6hxxqhe

Proving Concurrent Constraint Programming Correct, Revisited

Carlos Olarte, Elaine Pimentel
2015 Electronical Notes in Theoretical Computer Science  
In this paper, relying on a focusing discipline, we show that it is possible to give a logical characterization to different CCP-based languages with the highest level of adequacy.  ...  Concurrent Constraint Programming (CCP) is a simple and powerful model of concurrency where processes interact by telling and asking constraints into a global store of partial information.  ...  Moreover, in [16, 17] it is shown that considering ILL with subexponentials [3] as constraint systems allows for the specification of concurrent systems where epistemic, spatial and temporal modalities  ... 
doi:10.1016/j.entcs.2015.04.011 fatcat:gqaug2hesnhndnhe6zawimv2xa

Foundations for Reliable and Flexible Interactive Multimedia Scores [chapter]

Jaime Arias, Myriam Desainte-Catherine, Carlos Olarte, Camilo Rueda
2015 Lecture Notes in Computer Science  
For that, we propose a semantics based on tree-like structures representing the execution state of the score at each point in time.  ...  At execution time, the performer may modify the start/stop times of the TOs by triggering interaction points and the system guarantees that all the TRs are satisfied.  ...  On the other side, our logical characterization of ReactiveIS is based on the ideas in [10] where subexponentials in linear logic were used to give logical semantics to concurrent programming languages  ... 
doi:10.1007/978-3-319-20603-5_3 fatcat:6ho2qjwuurfdvd7ncyrdukk64q

On the Complexity of Linear Authorization Logics

Vivek Nigam
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
Finally, we argue by example that the latter fragment is natural and can be used in practice.  ...  On the other hand, we also identify a first-order fragment of LAL for which provability is PSPACE-complete.  ...  Cervesato and Scedrov [5] proposed a framework based on multiset rewriting (MSR) for specifying concurrent processes and also relate their system to linear logic provability.  ... 
doi:10.1109/lics.2012.61 dblp:conf/lics/Nigam12 fatcat:mpujo73eovhhjaosobmvkr273a

A Survey of the Proof-Theoretic Foundations of Logic Programming [article]

Dale Miller
2021 arXiv   pre-print
Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs.  ...  Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming.  ...  Acknowledgments: I thank Miroslaw Truszczynski and several anonymous reviewers for their comments on an earlier version of this paper.  ... 
arXiv:2109.01483v2 fatcat:fp3c746m5zaavd56ltn2d43kp4

Proving Structural Properties of Sequent Systems in Rewriting Logic [chapter]

Carlos Olarte, Elaine Pimentel, Camilo Rocha
2018 Lecture Notes in Computer Science  
They have been fully mechanized in Maude and have achieved a great degree of automation when used on several sequent systems including intuitionistic and classical logics, linear logic, and normal modal  ...  classical logic (G3cp), propositional linear logic (LL), and normal modal logics (K and S4).  ...  The work of the three authors was supported by CAPES, Colciencias, and INRIA via the STIC AmSud project "EPIC: EPistemic Interactive Concurrency" (Proc. No 88881.117603/2016-01).  ... 
doi:10.1007/978-3-319-99840-4_7 fatcat:ccjhxaulzzab7n24cps65k2ewm
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