Jiří Adámek, Horst Herrlich & George E. Strecker (1990):
Abstract and Concrete Categories: The Joy of Cats.
John Wiley and Sons.
Natasha Alechina, Michael Mendler, Valeria de Paiva & Eike Ritter (2001):
Categorical and Kripke Semantics for Constructive S4 Modal Logic.
In: Laurent Fribourg: Computer Science Logic (CSL'01),
LNCS 2142.
Springer,
pp. 292–307,
doi:10.1007/3-540-44802-0_21.
Steve Awodey (2010):
Category Theory,
second edition.
Oxford University Press.
Steve Awodey & Kohei Kishida (2008):
Topology and Modality: The Topological Interpretation of First-Order Modal Logic.
Review of Symbolic Logic 1,
pp. 146–166,
doi:10.1017/S1755020308080143.
Alexandru Baltag (2003):
A Coalgebraic Semantics for Epistemic Programs.
Electronic Notes in Theoretical Computer Science 82,
pp. 17–37,
doi:10.1016/S1571-0661(04)80630-3.
Alexandru Baltag & Lawrence Moss (2004):
Logics for Epistemic Programs.
Synthese 139,
pp. 165–224,
doi:10.1023/B:SYNT.0000024912.56773.5e.
Alexandru Baltag, Lawrence Moss & Sławomir Solecki (1998):
The Logic of Public Announcements, Common Knowledge and Private Suspicions.
In: Itzhak Gilboa: Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK VII),
pp. 43–56.
Available at http://www.tark.org/proceedings/tark_jul22_98/p43-baltag.pdf.
Johan van Benthem (2011):
Logical Dynamics of Information and Interaction.
Cambridge University Press,
doi:10.1017/CBO9780511974533.
Johan van Benthem, Jan van Eijck & Barteld Kooi (2006):
Logics of Communication and Change.
Information and Computation 204,
pp. 1620–1662,
doi:10.1016/j.ic.2006.04.006.
Patrick Blackburn, Maarten de Rijke & Yde Venema (2001):
Modal Logic.
Cambridge University Press,
doi:10.1017/CBO9781107050884.
Aurelio Carboni & Robert F. C. Walters (1987):
Cartesian Bicategories I.
Journal of Pure and Applied Algebra 49,
pp. 11–32,
doi:10.1016/0022-4049(87)90121-6.
Alexander Chagrov & Michael Zakharyaschev (1997):
Modal Logic.
Clarendon Press.
Corina Cîrstea, Alexander Kurz, Dirk Pattinson, Lutz Schröder & Yde Venema (2011):
Modal Logics are Coalgebraic.
The Computer Journal 54,
pp. 31–41,
doi:10.1093/comjnl/bxp004.
Corina Cîrstea & Mehrnoosh Sadrzadeh (2007):
Coalgebraic Epistemic Update Without Change of Model.
In: Till Mossakowski, Ugo Montanari & Magne Haveraaen: Algebra and Coalgebra in Computer Science (CALCO 2007),
LNCS 4642.
Springer,
pp. 158–172,
doi:10.1007/978-3-540-73859-6_11.
Bob Coecke & Éric Oliver Paquette (2011):
Categories for the Practising Physicist.
In: Bob Coecke: New Structures for Physics.
Springer,
pp. 173–286,
doi:10.1007/978-3-642-12821-9_3.
Hans van Ditmarsch, Wiebe van der Hoek & Barteld Kooi (2008):
Dynamic-Epistemic Logic.
Springer,
doi:10.1007/978-1-4020-5839-4.
Peter J. Freyd & Andre Scedrov (1990):
Categories, Allegories.
North-Holland.
Dov M. Gabbay, Valentin Shehtman & Dimitrij Skvortsov (2009):
Quantification in Nonclassical Logic 1.
Elsevier.
Silvio Ghilardi (2010):
Continuity, Freeness, and Filtrations.
Journal of Applied Non-Classical Logics 20,
pp. 193–217,
doi:10.3166/jancl.20.193-217.
David Harel, Dexter Kozen & Jerzy Tiuryn (2000):
Dynamic Logic.
MIT Press.
Claudio Hermida (2011):
A Categorical Outlook on Relational Modalities and Simulations.
Information and Computation 209,
pp. 1505–1517,
doi:10.1016/j.ic.2010.09.009.
Bart Jacobs (2016):
Introduction to Coalgebra: Towards Mathematics of States and Observation.
Cambridge University Press,
doi:10.1017/CBO9781316823187.
André Joyal & Myles Tierney (1984):
An Extension of the Galois Theory of Grothendieck.
American Mathematical Society.
Burghard von Karger (1998):
Temporal Algebra.
Mathematical Structures in Computer Science 8,
pp. 277–320,
doi:10.1017/S0960129598002540.
Kohei Kishida (2011):
Neighborhood-Sheaf Semantics for First-Order Modal Logic.
Electronic Notes in Theoretical Computer Science 278,
pp. 129–143,
doi:10.1016/j.entcs.2011.10.011.
Kohei Kishida (2013):
Public Announcements under Sheaves.
In: Yoichi Motomura, Alastair Butler & Daisuke Bekki: New Frontiers in Artificial Intelligence (JSAI-isAI 2012 Workshops),
LNCS 7856.
Springer,
pp. 96–108,
doi:10.1007/978-3-642-39931-2_8.
Kohei Kishida (forthcoming):
Categories and Modalities.
In: Elaine M. Landry: Categories for the Working Philosopher.
Oxford University Press.
Barteld Kooi (2007):
Dynamic Term-Modal Logic.
In: A Meeting of the Minds: Proceedings of the Workshop on Logic, Rationality and Interaction, Beijing, 2007.
College Publications,
pp. 173–185.
Clemens Kupke & Dirk Pattinson (2011):
Coalgebraic Semantics of Modal Logics: An Overview.
Theoretical Computer Science 412,
pp. 5070–5094,
doi:10.1016/j.tcs.2011.04.023.
Alexander Kurz & Alessandra Palmigiano (2013):
Epistemic Updates on Algebras.
Logical Methods in Computer Science 9(4):17,
doi:10.2168/LMCS-9(4:17)2013.
Stephen Lack (2010):
A 2-Categories Companion.
In: John C. Baez & J. Peter May: Towards Higher Categories.
Springer,
pp. 105–191,
doi:10.1007/978-1-4419-1524-5_4.
Joachim Lambek (1999):
Diagram Chasing in Ordered Categories with Involution.
Journal of Pure and Applied Algebra 143,
pp. 293–307,
doi:10.1016/S0022-4049(98)00115-7.
David K. Lewis (1968):
Counterpart Theory and Quantified Modal Logic.
Journal of Philosophy 65,
pp. 113–26,
doi:10.2307/2024555.
Minghui Ma (2011):
Mathematics of Public Announcements.
In: Hans van Ditmarsch, Jérôme Lang & Shier Ju: Logic, Rationality and Interaction: Third International Workhop, LORI 2011.
Springer,
pp. 193–205,
doi:10.1007/978-3-642-24130-7_14.
Saunders Mac Lane (1998):
Categories for the Working Mathematician,
second edition.
Springer-Verlag,
doi:10.1007/978-1-4757-4721-8.
Saunders Mac Lane & Ieke Moerdijk (1992):
Sheaves in Geometry and Logic: A First Introduction to Topos Theory.
Springer-Verlag,
doi:10.1007/978-1-4612-0927-0.
Lawrence S. Moss (1999):
Coalgebraic Logic.
Annals of Pure and Applied Logic 96,
pp. 277–317,
doi:10.1016/S0168-0072(98)00042-6.
Andrew M. Pitts (2000):
Categorical Logic.
In: Samson Abramsky, Dov M. Gabbay & Thomas S. E. Maibaum: Handbook of Logic in Computer Science, Volume 5: Algebraic and Logical Structures.
Oxford University Press,
pp. 39–128.
S. K. Thomason (1975):
Categories of Frames for Modal Logic.
Journal of Symbolic Logic 40,
pp. 439–442,
doi:10.2307/2272167.