A General Proof System for Modalities in Concurrent Constraint Programming

  • Vivek Nigam
  • Carlos Olarte
  • Elaine Pimentel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8052)


The combination of timed, spatial, and epistemic information is often needed in the specification of modern concurrent systems. We propose the proof system SELL\(^\Cap\), which extends linear logic with subexponentials with quantifiers over subexponentials, therefore allowing for an arbitrary number of modalities. We then show how a proper structure of the subexponential signature in SELL\(^\Cap\) allows for the specification of concurrent systems with timed, spatial, and epistemic modalities. In the context of Concurrent Constraint Programming (CCP), a declarative model of concurrency, we illustrate how the view of subexponentials as specific modalities is general enough to modularly encode into SELL\(^\Cap\) variants of CCP with these three modalities, thus providing a proof-theoretic foundations for those calculi.


Proof System Linear Logic Proof Theory Epistemic Modality Epistemic Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vivek Nigam
    • 1
  • Carlos Olarte
    • 2
  • Elaine Pimentel
    • 3
  1. 1.Universidade Federal da ParaíbaBrazil
  2. 2.Pontificia Universidad Javeriana-CaliColombia
  3. 3.Universidade Federal de Minas GeraisBrazil

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