Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-10T12:37:10.455Z Has data issue: false hasContentIssue false
  • English
  • Français

INQUISITIVE BISIMULATION

Part of: Model theory General logic

Published online by Cambridge University Press:  30 October 2020

IVANO CIARDELLI  and
MARTIN OTTO
IVANO CIARDELLI
Affiliation:
MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY (MCMP) LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN MUNICH, GERMANY E-mail: ivano.ciardelli@lmu.de
MARTIN OTTO
Affiliation:
DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITAET DARMSTADT DARMSTADT, GERMANY E-mail: otto@mathematik.tu-darmstadt.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures.

Keywords

inquisitive modal logicbisimulationteam semanticsvan Benthem theoremexpressive completenessmodel theory of modal logicsfinite model theory

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03B42: Logics of knowledge and belief (including belief change) 03C07: Basic properties of first-order languages and structures 03C80: Logic with extra quantifiers and operators 03C98: Applications of model theory 03B70: Logic in computer science

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 77 - 109
Check for updates
Copyright
© The Association for Symbolic Logic 2020

References

REFERENCES

Abramsky, S. and Väänänen, J., From IF to BI . Synthese , vol. 167 (2009), no. 2, pp. 207–230.CrossRefGoogle Scholar
Ciardelli, I., Modalities in the realm of questions: Axiomatizing inquisitive epistemic logic , Advances in Modal Logic (Goré, R., Kooi, B., and Kurucz, A., editors), College Publications, London, 2014, pp. 94–113.Google Scholar
Ciardelli, I., Questions in Logic , Volume DS-2016-01 of ILLC Dissertation Series, Institute for Logic, Language and Computation, Amsterdam, 2016.Google Scholar
Ciardelli, I., Dependency as question entailment , Dependence Logic: Theory and Applications (Abramsky, S., Kontinen, J., Väänänen, J., and Vollmer, H., editors), Springer International Publishing, 2016, pp. 129–181.CrossRefGoogle Scholar
Ciardelli, I., Questions as information types . Synthese , vol. 195 (2018), no. 1, pp. 321–365.CrossRefGoogle Scholar
Ciardelli, I., Groenendijk, J., and Roelofsen, F., Inquisitive semantics: A new notion of meaning . Language and Linguistics Compass , vol. 7 (2013), no. 9, pp. 459–476.CrossRefGoogle Scholar
Ciardelli, I., Groenendijk, J., and Roelofsen, F., On the semantics and logic of declaratives and interrogatives . Synthese , vol. 192 (2015), no. 6, pp. 1689–1728.CrossRefGoogle Scholar
Ciardelli, I. and Otto, M., Bisimulation in inquisitive modal logic , Theoretical Aspects of Rationality and Knowledge (Lang, J., editor), vol. 16. EPTCS, 2017. Google Scholar
Ciardelli, I. and Otto, M., Inquisitive bisimulation. Preprint, 2018, arXiv preprint, 57 pages, arXiv:1803.03483.Google Scholar
Ciardelli, I. and Roelofsen, F., Inquisitive logic . Journal of Philosophical Logic , vol. 40 (2011), pp. 55–94.CrossRefGoogle Scholar
Ciardelli, I. and Roelofsen, F., Inquisitive dynamic epistemic logic . Synthese , vol. 192 (2015), no. 6, pp. 1643–1687.CrossRefGoogle Scholar
Ciardelli, I., Groenendijk, J., and Roelofsen, F., Inquisitive Semantics , Oxford University Press, Oxford, 2018.CrossRefGoogle Scholar
Dawar, A. and Otto, M., Modal characterisation theorems over special classes of frames . Annals of Pure and Applied Logic , vol. 161 (2009), pp. 1–42.CrossRefGoogle Scholar
Galliani, P., Inclusion and exclusion dependencies in team semantics—on some logics of imperfect information . Annals of Pure and Applied Logic , vol. 163 (2012), no. 1, pp. 68–84.CrossRefGoogle Scholar
Goranko, V. and Otto, M., Model theory of modal logic , Handbook of Modal Logic (Blackburn, P., van Benthem, J., and Wolter, F., editors), Elsevier, 2007, pp. 249–329.CrossRefGoogle Scholar
Hansen, H. H., Monotone modal logics , MSc thesis, University of Amsterdam, 2003.Google Scholar
Hansen, H. H., Kupke, C., and Pacuit, E., Neighbourhood structures: Bisimilarity and basic model theory . Logical Methods in Computer Science , vol. 2 (2009), pp. 1–38. Google Scholar
Hintikka, J., Knowledge and Belief: An Introduction to the Logic of the Two Notions , Cornell University Press, Ithaca, 1962.Google Scholar
Hodges, W., Compositional semantics for a language of imperfect information . Logic Journal of IGPL , vol. 5 (1997), no. 4, pp. 539–563.CrossRefGoogle Scholar
Hodges, W., Some strange quantifiers , Structures in Logic and Computer Science , Lecture Notes in Computer Science, Springer, New York, 1997, pp. 51–65.CrossRefGoogle Scholar
Kontinen, J., Müller, J.-S., Schnoor, H., and Vollmer, H., A van Benthem theorem for modal team semantics, Proceedings of CSL 24. Leibniz International Proceedings in Informatics, 2015, pp. 277–291.Google Scholar
Meißner, S., On the model theory of inquisitive modal logic , Bachelor thesis. Department of Mathematics, TU Darmstadt, 2018.Google Scholar
Meißner, S. and Otto, M., A first-order framework for inquisitive modal logic. arXiv preprint, 2019, 16 pages, arXiv:1906.04981.Google Scholar
Otto, M., Elementary proof of the van Benthem–Rosen characterisation theorem. Technical report 2342, Fachbereich Mathematik, Technische Universität Darmstadt, 2004.Google Scholar
Otto, M., Modal and guarded characterisation theorems over finite transition systems . Annals of Pure and Applied Logic , vol. 130 (2004), pp. 173–205 CrossRefGoogle Scholar
Otto, M., Highly acyclic groups, hypergraph covers and the guarded fragment . Journal of the ACM , vol. 59 (2012), no. 1. https://dl.acm.org/doi/10.1145/2108242.2108247.CrossRefGoogle Scholar
Pacuit, E., Neighborhood Semantics for Modal Logic , Springer, New York, 2017 (forthcoming).CrossRefGoogle Scholar
Rosen, E., Modal logic over finite structures . Journal of Logic, Language and Information , vol. 6 (1997), pp. 427–439.CrossRefGoogle Scholar
Väänänen, J., Dependence Logic: A New Approach to Independence Friendly Logic , Cambridge University Press, Cambridge, MA, 2007.CrossRefGoogle Scholar
Väänänen, J., Modal dependence logic , New Perspectives on Games and Interaction (Apt, K. R. and van Rooij, R., editors), Amsterdam University Press, Amsterdam, 2008, pp. 237–254.Google Scholar
van Benthem, J., Modal Logic and Classical Logic , Napoli, Bibliopolis, 1983.Google Scholar
Yang, F., On extensions and variants of dependence logic: A study of intuitionistic connectives in the team semantics setting, Ph.D. thesis, University of Helsinki, 2014.Google Scholar
Yang, F. and Väänänen, J., Propositional logics of dependence . Annals of Pure and Applied Logic , vol. 167 (2016), pp. 557–589.CrossRefGoogle Scholar