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Bisimulation for Neighbourhood Structures [chapter]

Helle Hvid Hansen, Clemens Kupke, Eric Pacuit
Algebra and Coalgebra in Computer Science  
Our results include relational characterisations for 2 2 -bisimulation and neighbourhood bisimulation, and an analogue of Van Benthem's characterisation theorem for all three equivalence notions.  ...  correct notion of equivalence on neighbourhood structures.  ...  For monotonic neighbourhood structures, this question has already been addressed (cf.  ... 
doi:10.1007/978-3-540-73859-6_19 dblp:conf/calco/HansenKP07 fatcat:ipg2rzga6vemdetnzs4dmgd444

Neighbourhood Contingency Bisimulation [chapter]

Zeinab Bakhtiari, Hans van Ditmarsch, Helle Hvid Hansen
2016 Lecture Notes in Computer Science  
We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulationinvariant fragment of modal logic and of first-order logic, and  ...  The two sorts s and n correspond to states and to neighbourhoods, respectively, and the basic idea of viewing a neighbourhood model as a first-order L 1 -structure is to encode the neighbourhood function  ...  We introduce a notion of neighbourhood ∆-bisimilarity, inspired by the semantics of the ∆-modality and [9] , where different notions of structural invariance among neighbourhood models were studied.  ... 
doi:10.1007/978-3-662-54069-5_5 fatcat:hv3nn7r6trdntbakyy4nbqbiuy

Analysing Spatial Properties on Neighbourhood Spaces

Sven Linker, Fabio Papacchini, Michele Sevegnani, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces.  ...  Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.  ...  Regarding the existing extensions of SLCS with set-based modalities, we are interested in studying how far our notion of bisimulations imply the preservation of such modalities, and whether and how we  ... 
doi:10.4230/lipics.mfcs.2020.66 dblp:conf/mfcs/LinkerPS20 fatcat:y7mcuicnfzfureqgrvjxuwfzri

Analysing Spatial Properties on Neighbourhood Spaces [article]

Sven Linker and Fabio Papacchini and Michele Sevegnani
2020 arXiv   pre-print
We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces.  ...  Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.  ...  Bisimulations for Neighbourhood Spaces In this section we define two notions of bisimulation for neighbourhood spaces: neighbourhood bisimulation and path preserving bisimulation.  ... 
arXiv:2007.01266v1 fatcat:3chksixtubfjtcoca7l2gpjysa

ExpLOD: Summary-Based Exploration of Interlinking and RDF Usage in the Linked Open Data Cloud [chapter]

Shahan Khatchadourian, Mariano P. Consens
2010 Lecture Notes in Computer Science  
The bisimulation contractions are applied to subgraphs defined via queries, providing for summarization of arbitrary large or small graph neighbourhoods.  ...  ExpLOD's summaries are based on a novel mechanism that combines text labels and bisimulation contractions.  ...  We also thank the reviewers for their detailed comments.  ... 
doi:10.1007/978-3-642-13489-0_19 fatcat:sko4npquljbctem2gyfhwpu2da

Which Semantics for Neighbourhood Semantics?

Carlos Areces, Diego Figueira
2009 International Joint Conference on Artificial Intelligence  
Given Proposition 10, we can define the notion of N =bisimulation only for differentiated epistemic structures. Definition 11 (N = -bisimulation).  ...  ., D is the class of epistemic structures where every neighbourhood is the extension of a formula.  ...  Moreover, a simple notion of bisimulation exists for N = (E) and its satisfiability problem remains NP-complete.  ... 
dblp:conf/ijcai/ArecesF09 fatcat:mj75moecaraxzdmkd5vathxgfe

Bisimulations for coalgebras on Stone spaces

Sebastian Enqvist, Sumit Sourabh
2018 Journal of Logic and Computation  
We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4].  ...  The main result of our paper is that bisimulation for a Stone coalgebra is the topological closure of bisimulation for the underlying Set coalgebra.  ...  Relating neighbourhood bisimulations to Vietoris Bisimulations We now show neighbourhood bisimulations for P relate to Vietoris bisimulations.  ... 
doi:10.1093/logcom/exy001 fatcat:ks24sudl7zebpi3njgbzikle4q

A Modal Logic for Network Topologies [chapter]

Rogier M. van Eijk, Frank S. de Boer, Wiebe van der Hoek, John-Jules Ch. Meyer
2000 Lecture Notes in Computer Science  
We show that the language is semantically characterised by a generalisation of classical bisimulation, called history-based bisimulation, consider its decidability and study the application of the logic  ...  Example 12 (History-based bisimulation) To illustrate the notion of a history-based bisimulation, let us return to the structures Å and AE depicted in figure 3 , where we assume that the neighbourhood  ...  Theorem 15 (Semantic characterisation) Given two structures Å and AE , for all states Û from Å and Ù from AE the following holds: µ if Û Ù for some history-based bisimulation then for all sentences ³ ¾  ... 
doi:10.1007/3-540-40006-0_19 fatcat:ogj3nnfp5jhqpbvgivrw2pp4zy

Neighbourhood Structures: Bisimilarity and Basic Model Theory

Helle Hansen, Clemens Kupke, Eric Pacuit, Till Mossakowski
2009 Logical Methods in Computer Science  
structures, precocongruences are a better approximation of behavioural equivalence than 2^2-bisimulations.  ...  We give back-and-forth style characterisations for 2^2-bisimulations and precocongruences, we show that on a single coalgebra, precocongruences capture behavioural equivalence, and that between neighbourhood  ...  Peter Gumm for many fruitful discussions, and Yde Venema for initiating our cooperation on this subject. Special thanks also goes to the anonymous referees for useful comments and corrections.  ... 
doi:10.2168/lmcs-5(2:2)2009 fatcat:5tgcljiirrafpfn3lsbgway3ku

Bisimulation for Weakly Expressive Coalgebraic Modal Logics

Zeinab Bakhtiari, Helle Hvid Hansen, Marc Herbstritt
2017 Conference on Algebra and Coalgebra in Computer Science  
In this paper, we propose a notion of Λ-bisimulation which is parametric in a collection Λ of predicate liftings.  ...  However, for some applications, modal logics that are not expressive are of independent interest. Such an example is given by contingency logic.  ...  In particular, we see that if T is the neighbourhood functor and Λ consists of the usual neighbourhood modality, then Λ-bisimulation amounts to the notion of precocongruence for neighbourhood frames from  ... 
doi:10.4230/lipics.calco.2017.4 dblp:conf/calco/BakhtiariH17 fatcat:cd7kbpeigfekneqwvk5pjq2e6e

Neighbourhood semantics for graded modal logic [article]

Jinsheng Chen, Hans van Ditmarsch, Giuseppe Greco, Apostolos Tzimoulis
2021 arXiv   pre-print
We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames.  ...  We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.  ...  Each monotonic neighbourhood frame F = (W, {ν n } n∈N ) can be seen as a two-sorted relational structure (W, P(W), {R ν n } n∈N , R ∋ ) where R ν n ⊆ W × P(W) and R ∋ ⊆ P(W) × W such that wR ν n X iff  ... 
arXiv:2105.09202v1 fatcat:4cdpflm6m5badminye556tg5xi

A Coalgebraic Perspective on Monotone Modal Logic

Helle Hvid Hansen, Clemens Kupke
2004 Electronical Notes in Theoretical Computer Science  
In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.  ...  Then we investigate the relationship between the coalgebraic notions of equivalence and monotone bisimulation.  ...  For monotone (neighbourhood) models, monotone bisimulations have been presented in Pauly [28] , which also contains a number of results on the relationship between Kripke and monotone bisimulations together  ... 
doi:10.1016/j.entcs.2004.02.028 fatcat:sobmaoiz4renfnbkip6mii4vja

Exploring XML web collections with DescribeX

Mariano P. Consens, Renée J. Miller, Flavio Rizzolo, Alejandro A. Vaisman
2010 ACM Transactions on the Web  
An important trend is the need for increased flexibility in the structure of web documents.  ...  Even when XML web documents are valid with regard to a schema, the actual structure of such documents may exhibit significant variations across collections for several reasons: the schema may be very lax  ...  For neighbourhoods in that class, we can bypass the bisimulation computation and obtain the EEs directly from the LPath sets. Such is the class of the tree neighbourhoods.  ... 
doi:10.1145/1806916.1806920 fatcat:zbwam6cwtrespdhudcu2pednjm

Simulations and Bisimulations for Coalgebraic Modal Logics [chapter]

Daniel Gorín, Lutz Schröder
2013 Lecture Notes in Computer Science  
That is, for finitary set-based coalgebras, Λ-bisimulation works under strictly more general assumptions than T -bisimulation in the sense of Aczel and Mendler.  ...  We show that this notion is adequate in several ways: i) Λ-simulations preserve truth of positive formulas, ii) for Λ a separating set of monotone predicate liftings, the associated notion of Λ-bisimulation  ...  Acknowledgements We wish to thank Helle Hvid Hansen for useful pointers to the literature. Erwin R. Catesbeiana has voiced vague support for empty bisimulations.  ... 
doi:10.1007/978-3-642-40206-7_19 fatcat:gprfvxutw5g4nkh24wxbjoy2nu

Neighbourhood semantics for graded modal logic

Jinsheng Chen, Hans Van Ditmarsch, Giuseppe Greco, Apostolos Tzimoulis
2021 Bulletin of the Section of Logic  
We introduce a class of neighbourhood frames for graded modal logic using an operation from Kripke frames to neighbourhood frames.  ...  We also obtain a new definition of graded bisimulation by modifying the definition of monotonic bisimulation.  ...  Since (F • ) • = F for any graded neighbourhood frame F, F • K is equivalent to the class of all graded neighbourhood frames. Neighbourhood semantics for graded modal logic Theorem 4.4.  ... 
doi:10.18778/0138-0680.2021.12 fatcat:iyjvf4ehlzcg5dhurmlc2e5ir4
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