On subexponentials, focusing and modalities in concurrent systems
In this work we present the focused proof system SELLF⋒, which extends intuitionistic linear logic with subexponentials with the ability of quantifying over them, hence allowing for the use of an arbitrary number of modalities. We show that the view of subexponentials as specific modalities is gener...
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| Published in: | Theoretical computer science Vol. 693; pp. 35 - 58 |
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12.09.2017
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | In this work we present the focused proof system SELLF⋒, which extends intuitionistic linear logic with subexponentials with the ability of quantifying over them, hence allowing for the use of an arbitrary number of modalities. We show that the view of subexponentials as specific modalities is general enough to give a modular encoding of different flavors of Concurrent Constraint Programming (CCP), a simple and powerful model of concurrency. More precisely, we encode CCP calculi capturing time, spatial and epistemic behaviors into SELLF⋒, thus providing a proof theoretic foundation for those calculi and, at the same time, setting SELLF⋒ as a general framework for specifying such systems. |
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| AbstractList | In this work we present the focused proof system SELLF⋒, which extends intuitionistic linear logic with subexponentials with the ability of quantifying over them, hence allowing for the use of an arbitrary number of modalities. We show that the view of subexponentials as specific modalities is general enough to give a modular encoding of different flavors of Concurrent Constraint Programming (CCP), a simple and powerful model of concurrency. More precisely, we encode CCP calculi capturing time, spatial and epistemic behaviors into SELLF⋒, thus providing a proof theoretic foundation for those calculi and, at the same time, setting SELLF⋒ as a general framework for specifying such systems. |
| Author | Olarte, Carlos Nigam, Vivek Pimentel, Elaine |
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| Cites_doi | 10.1006/jsco.1996.0064 10.1016/j.tcs.2014.02.018 10.1093/logcom/2.3.297 10.1145/155183.155225 10.1016/j.entcs.2017.04.007 10.1006/inco.2000.3002 10.1007/s10817-010-9182-1 10.1016/0304-3975(87)90045-4 10.1016/S0304-3975(99)00231-5 10.1016/j.tcs.2009.07.041 10.1016/j.entcs.2015.04.011 10.1016/0167-6423(92)90005-V 10.1016/j.entcs.2014.06.008 10.1145/1149114.1149118 10.1007/s10601-013-9145-3 10.1017/S147106841400026X 10.1016/j.entcs.2011.03.009 10.1016/j.tcs.2015.06.031 10.3233/JCS-2004-12203 |
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| Snippet | In this work we present the focused proof system SELLF⋒, which extends intuitionistic linear logic with subexponentials with the ability of quantifying over... |
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| SubjectTerms | Concurrent constraint programming Linear logic Proof systems |
| Title | On subexponentials, focusing and modalities in concurrent systems |
| URI | https://dx.doi.org/10.1016/j.tcs.2017.06.009 |
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