An Adequate Compositional Encoding of Bigraph Structure in Linear Logic with Subexponentials
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9450)
In linear logic, formulas can be split into two sets: classical (those that can be used as many times as necessary) or linear (those that are consumed and no longer available after being used). Subexponentials generalize this notion by allowing the formulas to be split into many sets, each of which can then be specified to be classical or linear. This flexibility increases its expressiveness: we already have adequate encodings of a number of other proof systems, and for computational models such as concurrent constraint programming, in linear logic with subexponentials (). Bigraphs were proposed by Milner in 2001 as a model for ubiquitous computing, subsuming models of computation such as CCS and the \(\pi \)-calculus and capable of modeling connectivity and locality at the same time. In this work we present an encoding of the bigraph structure in , thus giving an indication of the expressive power of this logic, and at the same time providing a framework for reasoning and operating on bigraphs. Our encoding is adequate and therefore the operations of composition and juxtaposition can be performed on the logical level. Moreover, all the proof-theoretical tools of become available for querying and proving properties of bigraph structures.
KeywordsInference Rule Proof System Linear Logic Sequent Calculus Proof Search
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.
This work was partially supported by the ERC Advanced Grant ProofCert.
- 1.Beauquier, M., Schürmann, C.: A bigraph relational model. In: LFMTP, vol. 71 of EPTCS, pp. 14–28 (2011)Google Scholar
- 5.Chaudhuri, K.: Undecidability of multiplicative subexponential logic. In: 3rd LINEARITY, vol. 176 of EPTCS, pp. 1–8, July 2014Google Scholar
- 7.Grohmann, D., Miculan, M.: Directed bigraphs. ENTCS 173, 121–137 (2007)Google Scholar
- 8.Jensen, O.H., Milner, R.: Bigraphs and mobile processes (revised). Technical Report UCAM-CL-TR-580, University of Cambridge, February 2004Google Scholar
- 11.Nigam, V.: Exploiting non-canonicity in the sequent calculus. Ph.D. thesis, Ecole Polytechnique, September 2009Google Scholar
- 12.Nigam, V., Miller, D.: Algorithmic specifications in linear logic with subexponentials. In: PPDP, pp. 129–140 (2009)Google Scholar
- 13.Nigam, V., Olarte, C., Pimentel, E.: On subexponentials, focusing and modalities in concurrent systems. Draft Manuscript submitted for publication (2015)Google Scholar
- 14.Nigam, V., Pimentel, E., Reis, G.: An extended framework for specifying and reasoning about proof systems. J. of Logic Comput. (2014). doi: 10.1093/logcom/exu029, http://logcom.oxfordjournals.org/content/early/2014/06/06/logcom.exu029
© Springer-Verlag Berlin Heidelberg 2015