A general proof system for modalities in concurrent constraint programming

  • Authors:

  • Vivek Nigam;Carlos Olarte;Elaine Pimentel

  • Affiliations:

  • Universidade Federal da Paraíba, Brazil;Pontificia Universidad Javeriana-Cali, Colombia;Universidade Federal de Minas Gerais, Brazil

  • Venue:
  • CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
  • Year:
  • 2013

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Abstract

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.