Navegando por Autor "Nigam, Vivek"

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Dynamic spaces in concurrent constraint programming
(Elsevier, 2014) Nigam, Vivek; Pimentel, Elaine Gouvea; Vega, Carlos Alberto Olarte
Concurrent constraint programming (CCP) is a declarative model for concurrency where agents interact with each other by posting (telling) and asking constraints (formulas in logic) in a shared store of partial information. With the advent of emergent applications as security protocols, social networks and cloud computing, the CCP model has been extended in different directions to faithfully model such systems as follows: (1) It has been shown that a name-passing discipline, where agents can communicate local names, can be described through the interplay of local (∃) processes along with universally (∀) quantified asks. 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 in CCP has been enhanced with local stores for the specification of distributed spaces. Then, agents are allowed to share some information with others but keep some facts for themselves. Recently, we have shown that local stores can be neatly represented in CCP by considering a constraint system where constraints are built from a fragment of linear logic with subexponentials (SELL). In this paper, we explore the use of existential (⋓) and universal (⋒) quantification over subexponentials in SELL in order to endow CCP with the ability to communicate location (space) names. The resulting CCP language that we obtain is a model of distributed computation where it is possible to dynamically establish new shared spaces for communication. We thus extend the sort of mobility achieved in (1) –for variables – to dynamically change the shared spaces among agents – (2) above. Finally, we argue that the new CCP language can be used in the specification of service oriented computing systems
Mechanizing focused linear logic in coq
(Elsevier, 2018) Xavier, Bruno; Vega, Carlos Alberto Olarte; Reis, Giselle; Nigam, Vivek
Linear logic has been used as a foundation (and inspiration) for the development of programming languages, logical frameworks and models for concurrency. Linear logic's cut-elimination and the completeness of focusing are two of its fundamental properties that have been exploited in such applications. Cut-elimination guarantees that linear logic is consistent and has the so-called sub-formula property. Focusing is a discipline for proof search that was introduced to reduce the search space, but has proved to have more value, as it allows one to specify the shapes of proofs available. This paper formalizes first-order linear logic in Coq and mechanizes the proof of cut-elimination and the completeness of focusing. Moreover, the implemented logic is used to encode an object logic, such as in a linear logical framework, and prove adequacy
A proof theoretic study of soft concurrent constraint programming
(Cambridge University Press, 2014) Pimentel, Elaine Gouvea; Nigam, Vivek; Vega, Carlos Alberto Olarte
Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic. In fact, the underlying constraint system can be built from a suitable fragment of intuitionistic (linear) logic -ILL- and processes can be interpreted as formulas in ILL. Constraints as ILL formulas fail to represent accurately situations where “preferences” (called soft constraints) such as probabilities, uncertainty or fuzziness are present. In order to circumvent this problem, c-semirings have been proposed as algebraic structures for defining constraint systems where agents are allowed to tell and ask soft constraints. Nevertheless, in this case, the tight connection to logic and proof theory is lost. In this work, we give a proof theoretical meaning to soft constraints: they can be defined as formulas in a suitable fragment of ILL with subexponentials (SELL) where subexponentials, ordered in a c-semiring structure, are interpreted as preferences. We hence achieve two goals: (1) obtain a CCP language where agents can tell and ask soft constraints and (2) prove that the language in (1) has a strong connection with logic. Hence we keep a declarative reading of processes as formulas while providing a logical framework for soft-CCP based systems. 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
Subexponential concurrent constraint programming
(Elsevier, 2015) Pimentel, Elaine Gouvea; Nigam, Vivek; Vega, Carlos Alberto Olarte
In previous works we have shown that linear logic with subexponentials (SELL), a refinement of linear logic, can be used to specify emergent features of concurrent constraint programming (CCP) languages, such as preferences and spatial, epistemic and temporal modalities. 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 of preferences. These results provided clear proof theoretic foundations to existing systems. This paper goes in the opposite direction, answering positively the question: can the proof theory of linear logic with subexponentials contribute to the development of new CCP languages? We propose a CCP language with the following powerful features: 1) computational spaces where agents can tell and ask preferences (soft-constraints); 2) systems where spatial and temporal modalities can be combined; 3) shared spaces for communication that can be dynamically established; and 4) systems that can dynamically create nested spaces. In order to provide the proof theoretic foundations for such a language, we propose a unified logical framework (SELLS) combining the extensions of linear logic with subexponentials mentioned above, and showing that this new framework has interesting proof theoretical properties such as cut-elimination and a sound and complete focused proof system

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Navegando por Autor "Nigam, Vivek"