Cited By
View all- Bussi LCiancia VGadducci F(2023)A Spatial Logic with Time and QuantifiersDynamic Logic. New Trends and Applications10.1007/978-3-031-51777-8_1(1-19)Online publication date: 15-Sep-2023
On Binding in the Spatial Logics for Closure Spaces
Authors: 
Laura Bussi, Vincenzo Ciancia, Fabio Gadducci, Diego Latella, Mieke MassinkAuthors Info & Claims
Laura Bussi, Vincenzo Ciancia, Fabio Gadducci, Diego Latella, Mieke MassinkAuthors Info & ClaimsPages 479 - 497
Abstract
We present two different extensions of the spatial logic for closure spaces (SLCS), and its spatio-temporal variant (SLCS), with spatial quantification operators. The first concerns the existential quantification on individual points of a space. The second concerns the quantification on sets of points. The latter amounts to a form of quantification over atomic propositions, thus without the full power of second order logic. The spatial quantification operators are useful for reasoning about the existence of particular spatial objects in a space, their spatial relation with respect to other spatial objects, and, in the spatio-temporal setting, to reason about the dynamic evolution of such spatial objects in time and space, including reasoning about newly introduced items. In this preliminary study we illustrate the expressiveness of the operators by means of several small, but representative, examples.
References
[1]
Baldan P, Corradini A, König B, and Lluch Lafuente A Fiadeiro JL and Schobbens P-Y A temporal graph logic for verification of graph transformation systems Recent Trends in Algebraic Development Techniques 2007 Heidelberg Springer 1-20
[2]
Bednarczyk, B., Demri, S.: Why propositional quantification makes modal logics on trees robustly hard? In: LICS 2019, pp. 1–13. IEEE (2019)
[3]
Belmonte, G., Broccia, G., Ciancia, V., Latella, D., Massink, M.: Feasibility of spatial model checking for nevus segmentation. In: Bliudze, S., Gnesi, S., Plat, N., Semini, L. (eds.) FormaliSE@ICSE 2021, pp. 1–12. IEEE (2021)
[4]
Belmonte G, Ciancia V, Latella D, and Massink M ter Beek MH, Fantechi A, and Semini L Innovating medical image analysis via spatial logics From Software Engineering to Formal Methods and Tools, and Back 2019 Cham Springer 85-109
[5]
Belmonte G, Ciancia V, Latella D, and Massink M Vojnar T and Zhang L VoxLogicA: a spatial model checker for declarative image analysis Tools and Algorithms for the Construction and Analysis of Systems 2019 Cham Springer 281-298
[6]
van Benthem J and Bezhanishvili G Aiello M, Pratt-Hartmann I, and van Benthem J Modal logics of space Handbook of Spatial Logics 2007 Dordrecht Springer 217-298
[7]
Bezhanishvili, N., Ciancia, V., Gabelaia, D., Grilletti, G., Latella, D., Massink, M.: Geometric model checking of continuous space. CoRR arXiv:abs/2105.06194 (2021)
[8]
Bull RA On modal logic with propositional quantifiers J. Symb. Log. 1969 34 2 257-263
[9]
Buonamici FB, Belmonte G, Ciancia V, Latella D, and Massink M Spatial logics and model checking for medical imaging Int. J. Softw. Tools Technol. Transf. 2020 22 2 195-217
[10]
Bussi L, Ciancia V, and Gadducci F Peters K and Willemse TAC Towards a spatial model checker on GPU Formal Techniques for Distributed Objects, Components, and Systems 2021 Cham Springer 188-196
[11]
Bussi, L., Ciancia, V., Gadducci, F., Latella, D., Massink, M.: Towards model checking video streams using VoxLogicA on GPU’s. In: DataMod 2021. LNCS, Springer, Cham (2022, to appear)
[12]
Ciancia V, Gilmore S, Grilletti G, Latella D, Loreti M, and Massink M Spatio-temporal model checking of vehicular movement in public transport systems Int. J. Softw. Tools Technol. Transf. 2018 20 3 289-311
[13]
Ciancia V, Grilletti G, Latella D, Loreti M, and Massink M Bianculli D, Calinescu R, and Rumpe B An experimental spatio-temporal model checker Software Engineering and Formal Methods 2015 Heidelberg Springer 297-311
[14]
Ciancia V, Latella D, Loreti M, and Massink M Diaz J, Lanese I, and Sangiorgi D Specifying and verifying properties of space Theoretical Computer Science 2014 Heidelberg Springer 222-235
[15]
Ciancia, V., Latella, D., Loreti, M., Massink, M.: Model checking spatial logics for closure spaces. J. Log. Methods Comput. Sci. 12(4) (2016)
[16]
Ciancia V, Latella D, Massink M, Paškauskas R, and Vandin A Margaria T and Steffen B A tool-chain for statistical spatio-temporal model checking of bike sharing systems Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques 2016 Cham Springer 657-673
[17]
Ciancia, V., Latella, D., Massink, M., de Vink, E.P.: On bisimilarities for closure spaces - preliminary version. CoRR arXiv:abs/2105.06690 (2021)
[18]
Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3) (2009)
[19]
Gadducci F, Lluch-Lafuente A, and Vandin A Counterpart semantics for a second-order -calculus Fund. Inform. 2012 118 1–2 177-205
[20]
Galton A A generalized topological view of motion in discrete space Theoret. Comput. Sci. 2003 305 1–3 111-134
[21]
Grosu R, Smolka SA, Corradini F, Wasilewska A, Entcheva E, and Bartocci E Learning and detecting emergent behavior in networks of cardiac myocytes Commun. ACM 2009 52 3 97-105
[22]
Haghighi, I., Jones, A., Kong, Z., Bartocci, E., Grosu, R., Belta, C.: Spatel: a novel spatial-temporal logic and its applications to networked systems. In: Girard, A., Sankaranarayanan, S. (eds.) HSCC 2015, pp. 189–198. ACM (2015)
[23]
Holliday WH A note on algebraic semantics for S5 with propositional quantifiers Notre Dame J. Formal Log. 2017 60 2 321-332
[24]
Kripke SA A completeness theorem in modal logic J. Symb. Log. 1959 24 1 1-14
[25]
Kröger F and Merz S Kröger F and Merz S First-order linear temporal logic Temporal Logic and State Systems 2008 Heidelberg Springer 153-179
[26]
Kurtonina N and de Rijke M Bisimulations for temporal logic J. Logic Lang. Inform. 1997 6 4 403-425
[27]
Loreti, M., Quadrini, M.: A spatial logic for a simplicial complex model. CoRR arXiv:abs/2105.08708 (2021)
[28]
Nenzi, L., Bortolussi, L., Ciancia, V., Loreti, M., Massink, M.: Qualitative and quantitative monitoring of spatio-temporal properties with SSTL. J. Log. Methods Comput. Sci. 14(4) (2018)
[29]
Patthak A, Bhattacharya I, Dasgupta A, Dasgupta P, and Chakrabarti P Quantified computation tree logic Inf. Process. Lett. 2002 82 3 123-129
[30]
Rensink A Baier C and Hermanns H Model checking quantified computation tree logic CONCUR 2006 – Concurrency Theory 2006 Heidelberg Springer 110-125
[31]
Smyth MB and Webster J Aiello M, Pratt-Hartmann I, and van Benthem J Discrete spatial models Handbook of Spatial Logics 2007 Dordrecht Springer 713-798
[32]
Stirling C Abramsky S, Gabbay D, and Maibaum T Modal and temporal logics Handbook of Logic in Computer Science 1993 Oxford Oxford University Press 477-563
[33]
Čech, E.: Topological spaces. In: Pták, V. (ed.) Topological Spaces, chap. III, pp. 233–394. Publishing House of the Czechoslovak Academy of Sciences/Interscience Publishers, Wiley, Prague/London-New York-Sydney (1966). Revised edition by Z. Frolíc, M. Katětov. Scientific editor, V. Pták. Editor of the English translation, C.O. Junge. MR0211373
Index Terms
- On Binding in the Spatial Logics for Closure Spaces
Index terms have been assigned to the content through auto-classification.
Recommendations
Denotational Semantics for Modal Systems S3---S5 Extended by Axioms for Propositional Quantifiers and Identity
There are logics where necessity is defined by means of a given identity connective: $${\square\varphi := \varphi\equiv\top}$$ := ($${\top}$$ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity (PI) $${...
Formalizing and Computing Propositional Quantifiers
CPP 2023: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and ProofsA surprising result of Pitts (1992) says that propositional quantifiers are definable internally in intuitionistic propositional logic (IPC). The main contribution of this paper is to provide a formalization of Pitts’ result in the Coq proof assistant,...
Δ-core Fuzzy Logics with Propositional Quantifiers, Quantifier Elimination and Uniform Craig Interpolation
In this paper we investigate the connections between quantifier elimination, decidability and Uniform Craig Interpolation in Δ-core fuzzy logics added with propositional quantifiers. As a consequence, we are able to prove that several propositional ...
Comments
Information & Contributors
Information
Published In
Oct 2022
607 pages
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 22 October 2022
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 03 Jan 2025
Other Metrics
Citations
Cited By
View all- Bussi LCiancia VGadducci F(2023)A Spatial Logic with Time and QuantifiersDynamic Logic. New Trends and Applications10.1007/978-3-031-51777-8_1(1-19)Online publication date: 15-Sep-2023