{"type":"ScholarlyArticle","title":"Intuitionistic Layered Graph Logic","authors":[{"name":"Simon Docherty","slug":"simon-docherty","given":"Simon","family":"Docherty","affiliation":"University College London"},{"name":"David Pym","slug":"david-pym","given":"David","family":"Pym","affiliation":"University College London"}],"abstract":"Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in other bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give a soundness and completeness theorem for a labelled tableaux system with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied.","doi":"10.24963/ijcai.2017/673","url":"https://ijcai.org/proceedings/2017/673","pdf":"https://ijcai.org/proceedings/2017/0673.pdf","markdown":"https://ijcai.org/proceedings/2017/673.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/673","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Best Sister Conferences","track":"Best Sister Conferences","number":673,"pages":{"first":4816,"last":4820},"keywords":["Artificial Intelligence: knowledge representation and reasoning","Artificial Intelligence: other"],"videos":[],"references":[{"position":1,"raw":"[Anderson and Pym, 2016] G. Anderson and D. Pym. A cal- culus and logic of bunched resources and processes. The- oretical Computer Science, 614(63):63 -96, 2016.","title":"A calculus and logic of bunched resources and processes","authors":"G Anderson, D Pym","year":"2016","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bezhanishvili and de Jongh, 2006] N. Bezhanishvili and D. de Jongh. Intuitionistic logic. Technical Report PP- 2006-25, Institute for Logic, Language and Computation. Universiteit van Amsterdam, 2006.","title":"Intuitionistic logic","authors":"N Bezhanishvili, D De Jongh","year":"2006","venue":"Language and Computation","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bródka et al., 2011] P. Bródka, K. Skibicki, P. Kazienko, and K. Musiał. A degree centrality in multi-layered social network. In International Conference on Computational Aspects of Social Networks, 2011.","title":"A degree centrality in multi-layered social network","authors":"P Bródka, K Skibicki, P Kazienko, K Musiał","year":"2011","venue":"International Conference on Computational Aspects of Social Networks","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Collinson and Pym, 2009] M. Collinson and D. Pym. Alge- bra and logic for resource-based systems modelling. Math- ematical Structures In in Computer Science, 19(5):959 - 1027, 2009.","title":"Algebra and logic for resource-based systems modelling","authors":"M Collinson, D Pym","year":"2009","venue":"Mathematical Structures In in Computer Science","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Collinson et al., 2012] M. Collinson, B. Monahan, and D. Pym. A Discipline of Mathematical Systems Modelling. College Publications, 2012.","title":"A Discipline of Mathematical Systems Modelling","authors":"M Collinson, B Monahan, D Pym","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Collinson et al., 2014] M. Collinson, K. McDonald, and D. Pym. A substructural logic for layered graphs. Jour- nal of Logic and Computation, 24(4):953 -988, 2014. doi=10.1093/logcom/exv019.","title":"A substructural logic for layered graphs","authors":"M Collinson, K Mcdonald, D Pym","year":"2014","venue":"Journal of Logic and Computation","doi":"=10.1093/logcom/exv019","url":null,"internal_url":null},{"position":7,"raw":"[Collinson et al., 2015] M. Collinson, K. McDonald, and D. Pym. Layered graph logic as an assertion language for access control. Journal of Logic and Computation, 2015. doi=10.1093/logcom/exv020.","title":"Layered graph logic as an assertion language for access control","authors":"M Collinson, K Mcdonald, D Pym","year":"2015","venue":"Journal of Logic and Computation","doi":"=10.1093/logcom/exv020","url":null,"internal_url":null},{"position":8,"raw":"[Courtault and Galmiche, 2015] J.-R. Courtault and D. Galmiche. A modal separation logic for resource dynamics. Journal of Logic and Computation, 2015. doi=10.1093/logcom/exv031.","title":"A modal separation logic for resource dynamics","authors":"J.-R Courtault, D Galmiche","year":"2015","venue":"Journal of Logic and Computation","doi":"=10.1093/logcom/exv031","url":null,"internal_url":null},{"position":9,"raw":"[Fiat et al., 1998] A. Fiat, D. Foster, H. Karloff, Y. Rabani, Y. Ravid, and S. Vishwanathan. Competitive algorithms for layered graph traversal. SIAM Journal on Computing, 28(2):447-462, 1998.","title":"Competitive algorithms for layered graph traversal","authors":"A Fiat, D Foster, H Karloff, Y Rabani, Y Ravid, S Vishwanathan","year":"1998","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fitting, 1972] M. Fitting. Tableau methods of proof for modal logics. Notre Dame Journal of Formal Logic, 13(2):237 -247, 1972.","title":"Tableau methods of proof for modal logics","authors":"M Fitting","year":"1972","venue":"Notre Dame Journal of Formal Logic","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Galmiche et al., 2005] D. Galmiche, D. Méry, and D. Pym. The semantics of BI and resource tableaux. Mathematical Structures in Computer Science, 15(06):1033-1088, 2005.","title":"The semantics of BI and resource tableaux","authors":"D Galmiche, D Méry, D Pym","year":"2005","venue":"Mathematical Structures in Computer Science","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Girard, 1987] J.-Y. Girard. Linear logic. Theoretical Com- puter Science, 50(1):1 -101, 1987.","title":"Linear logic","authors":"J.-Y Girard","year":"1987","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gouveia et al., 2011] L. Gouveia, L. Simonetti, and E. Uchoa. Modeling hop-constrained and diameter- constrained minimum spanning tree problems as steiner tree problems over layered graphs. Mathematical Programming, 128(1):123 -148, 2011.","title":"Modeling hop-constrained and diameterconstrained minimum spanning tree problems as steiner tree problems over layered graphs","authors":"L Gouveia, L Simonetti, E Uchoa","year":"2011","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kripke, 1965] S. A. Kripke. A semantical analysis of intu- itionistic logic I. Studies in Logic and the Foundations of Mathematics, 40:92-130, 1965.","title":"A semantical analysis of intuitionistic logic I","authors":"S A Kripke","year":"1965","venue":"Studies in Logic and the Foundations of Mathematics","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kurant and Thiran, 2006] M. Kurant and P. Thiran. Layered complex networks. Physical Review Letters, 96(138701), 2006.","title":"Layered complex networks","authors":"M Kurant, P Thiran","year":"2006","venue":"Physical Review Letters","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lambek, 1993] J. Lambek. From categorical grammar to bi- linear logic. In P. Schroeder-Heister and K. Došen, editors, Substructural Logics, pages 207 -237. Oxford University Press, 1993.","title":"From categorical grammar to bilinear logic","authors":"J Lambek","year":"1993","venue":"Substructural Logics","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Larchey-Wendling, 2014] D. Larchey-Wendling. The for- mal proof of the strong completeness of partial monoidal Boolean BI. Journal of Logic and Computation, 2014. doi=10.1093/logcom/exu031.","title":"The formal proof of the strong completeness of partial monoidal Boolean BI","authors":"D Larchey-Wendling","year":"2014","venue":"Journal of Logic and Computation","doi":"=10.1093/logcom/exu031","url":null,"internal_url":null},{"position":18,"raw":"[Maus et al., 2011] C. Maus, S. Rybacki, and A. M. Uhrma- cher. Rule-based multi-level modeling of cell biolog- ical systems. BMC Systems Biology, 5(166), 2011. doi=10.1186/1752-0509-5-166.","title":"Rule-based multi-level modeling of cell biological systems","authors":"C Maus, S Rybacki, A M","year":null,"venue":"BMC Systems Biology","doi":"2011.doi=10.1186/1752-0509-5-166","url":null,"internal_url":null},{"position":19,"raw":"[Milner, 2009] R. Milner. The Space and Motion of Commu- nicating Agents. Cambridge University Press, 2009.","title":"The Space and Motion of Communicating Agents","authors":"R Milner","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[O'Hearn and Pym, 1999] P. O'Hearn and D. Pym. The logic of bunched implications. Bulletin of Symbolic Logic, 5(2):215-244, 1999.","title":"The logic of bunched implications","authors":"O'hearn, ; P Pym, D O'hearn, Pym","year":"1999","venue":"Bulletin of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Papadimitriou and Yannakakis, 1991] C. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoretical Computer Science, 84(1):127 -150, 1991.","title":"Shortest paths without a map","authors":"C Papadimitriou, M Yannakakis","year":"1991","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Paz, 2011] A. Paz. A theory of decomposition into prime factors of layered interconnection networks. Discrete Ap- plied Mathematics, 159(7):628-646, 2011.","title":"A theory of decomposition into prime factors of layered interconnection networks","authors":"A Paz","year":"2011","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Pym et al., 2004] D. Pym, P. O'Hearn, and H. Yang. Possi- ble worlds and resources: the semantics of BI. Theoretical Computer Science, 315(1):257-305, 2004.","title":"Possible worlds and resources: the semantics of BI","authors":"D Pym, P O'hearn, H Yang","year":"2004","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Schneier, 2005] B. Schneier. The weakest link. (https: //www.schneier.com/blog/archives/2005/ 02/the_weakest_lin.html), 2005.","title":"The weakest link","authors":"B Schneier","year":"2005","venue":null,"doi":null,"url":"https://www.schneier.com/blog/archives/2005/02/the_weakest_lin.html","internal_url":null},{"position":25,"raw":"[Wang et al., 2009] H. Wang, J. Wang, and P. de Wilde. Topological analysis of a two coupled evolving networks model for business systems. Expert Systems with Applica- tions, 36(5):9548 -9556, 2009.","title":"Topological analysis of a two coupled evolving networks model for business systems","authors":"H Wang, J Wang, P De Wilde","year":"2009","venue":"Expert Systems with Applications","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}