Published: 6th March 2017
DOI: 10.4204/EPTCS.243
ISSN: 2075-2180


Proceedings of the Ninth Workshop on
Methods for Modalities
Indian Institute of Technology, Kanpur, India, 8th to 10th January 2017

Edited by: Sujata Ghosh and R. Ramanujam

Invited Presentation: A Gentle Introduction to Epistemic Planning: The DEL Approach
Thomas Bolander
Invited Presentation: Deterministic Temporal Logics and Interval Constraints
Kamal Lodaya and Paritosh K. Pandya
Invited Presentation: Modal Logics of Tychonoff HED-spaces
Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan and Jan van Mill
Invited Presentation: Finite Model Reasoning in Expressive Fragments of First-Order Logic
Lidia Tendera
Temporal Justification Logic
Samuel Bucheli, Meghdad Ghari and Thomas Studer
Cooperative Epistemic Multi-Agent Planning for Implicit Coordination
Thorsten Engesser, Thomas Bolander, Robert Mattmüller and Bernhard Nebel
Graphical Sequent Calculi for Modal Logics
Minghui Ma and Ahti-Veikko Pietarinen
Strong Completeness and the Finite Model Property for Bi-Intuitionistic Stable Tense Logics
Katsuhiko Sano and John G. Stell


This volume consists of papers and tutorials presented at the Ninth Workshop on Methods for Modalities held at the Indian Institute of Technology, Kanpur, India from January 8 to 9, 2017.

Methods for Modalities is a workshop series aimed at bringing together researchers interested in developing proof methods, verification methods, algorithms and tools based on modal logic. Here the term ''modal logics'' is conceived broadly, including description logic, guarded fragments, conditional logic, temporal and hybrid logics, dynamic logic and others. The first workshop was held in May 1999 in Amsterdam, and since then it has travelled the world. The 9th workshop was co-located with the Indian Conference on Logic and its Applications (ICLA), January 5 to 7, 2017.

We had five eminent invited speakers in this edition of the workshop. Lidia Tendera spoke on expressive fragments of first-order logic, Joel Gregory Lucero-Bryan on modal logics of topological spaces. Thomas Bolander gave a detailed tutorial on epistemic planning, while Kamal Lodaya and Paritosh Pandya gave a tutorial introduction to deterministic temporal logics. We thank these speakers for insightful presentations, which have been included as abstracts / papers here.

We are very grateful for having the cooperation and advice of 13 other members of the program committee: Carlos Areces (Universidad Nacional de Cordoba), Mohua Banerjee (IIT Kanpur), Nick Bezhanishvili (University of Amsterdam), Torben Brauner (Roskilde University), Hans van Ditmarsch (LORIA, Nancy), Tim French (The University of Western Australia, Perth), Davide Grossi (University of Liverpool), Agi Kurucz (King's College, London), Yongmei Liu (Sun Yat Sen University, Guangzhou), Claudia Nalon (Universidade de Brasilia), Paritosh Pandya (TIFR Mumbai), Sunil Easaw Simon (IIT Kanpur) and Yde Venema (University of Amsterdam). We thank them for their hard work in providing careful reviews and for the detailed discussions about the submissions.

The organizing team at IIT, Kanpur, led by Anil Seth, did an excellent job of running the workshop, we thank them all.

We thank Rob van Glabbeek for his help with the EPTCS proceedings, and Anantha Padmanabha (IMSc, Chennai) for help with preparing this volume.

Sujata Ghosh, Indian Statistical Institute, Chennai

R. Ramanujam, Institute of Mathematical Sciences, Chennai

(Programme Co-Chairs, M4M9)

Modal Logics of Tychonoff HED-spaces

Guram Bezhanishvili
Nick Bezhanishvili
Joel Lucero-Bryan
Jan van Mill

Topological semantics interprets modal box as topological interior, and hence modal diamond as topological closure. Topological semantics is a natural generalization of Kripke semantics for the well-known modal system S4 since an S4-frame can be viewed as a (special) topological space. Therefore, every Kripke complete extension of S4 is also topologically complete. However, topological spaces arising from S4-frames lack good separation properties. Thus, it is desirable to know which modal logics arise from topological spaces satisfying good separation axioms, such as Tychonoff spaces. This turns out to be a rather nontrivial problem to solve.

In this talk we concentrate on the well-known modal logic S4.3 which is obtained from S4 by postulating the axiom □(□p → q) V □(□q → p). The Bull-Fine theorem states that there are countably many extensions of S4.3, each of which is finitely axiomatizable and has the finite model property (see e.g. [2]). The modal logic S4.3 is the logic of all hereditarily extremally disconnected (HED) spaces [1]. We introduce the concept of a Zemanian extension of S4.3 by generalizing the Zeman modal logic. By utilizing the Bull-Fine theorem we prove that an extension of S4.3 is the logic of a Tychonoff HED-space iff it is Zemanian. This solves the aforementioned problem for extensions of S4.3.


  1. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan & J van Mill (2015): S4.3 and hereditarily extremally disconnected spaces. Georgian Mathematical Journal 22(4), pp. 469– 475, doi:10.1515/gmj-2015-0041.
  2. K. Fine (1971): The logics containing S4.3. Z. Math. Logik Grundlagen Math. 17, pp. 371–376, doi:10.1002/malq.19710170141.