NASSLLI18 Course : Beyond “knowing that”: a new generation of epistemic logics

Lecturer: Yanjing Wang (王彦晶) Department of Philosophy, Peking University

Epistemic logic is a major field of philosophical logic studying reasoning patterns about knowledge. Despite its various applications in epistemology, theoretical computer science, AI, and game theory, the technical developments in the field have been mainly focusing on the propositional part, i.e., the propositional modal logics of “knowing that”. However, knowledge is also expressed in natural language by “knowing whether”, “knowing what”, “knowing how”, “knowing why” and so on (know-wh hereafter). Recent years witnessed a growing interest in non-standard epistemic logics of know-wh motivated by questions in philosophy, AI, and linguistics. Inspired by linguistic discussions on the semantics of questions, the new epistemic modalities introduced in those logics often share, in their formal semantics, the general schema of ‘exists x K phi’ (where K is the knowledge modality). For example, knowing how to achieve phi roughly says that there exists a way such that you know that it is a way to make sure that phi. The axioms of those logics intuitively capture the essential interactions of know-that and other know-wh operators, and the resulting logics are decidable. 

A slightly outdated survey: Yanjing Wang: Beyond Knowing That: A New Generation of Epistemic Logics, in Jaakko Hintikka on knowledge and game-theoretical semantics, Springer, 12: 499—533, 2018

In this course, I will survey the recent developments of this new research program on non-standard epistemic logics of know-wh and its various connections with existing logics and philosophical/AI/linguistic questions in the literature. Inspired by those logics, we will also discuss a very general and powerful framework based on a predicate language extended by new modalities which pack a quantifier and a modality together. We show that the resulting logic, though more expressive, shares many good properties of the basic propositional modal logic, such as the finite-tree-model property. This may also pave a new way to the discovery of new decidable fragments of first-order modal logic.

Check the website of the previous ESSLLI15 course for an (outdated) preview of the course. 

Day 1 Introduction (Slides)

Main Ref (besides the “usual suspects”):

  • Hintikka, J., Hintikka, M.: Reasoning about knowledge in philosophy: The paradigm of epistemic logic. In: The Logic of Epistemology and the Epistemology of Logic. Volume 200 of Synthese Library. Springer Netherlands (1989) 17–35
  • Yanjing Wang: Beyond knowing that: a new generation of epistemic logic (arXiv) in Jaakko Hintikka on knowledge and game theoretical semantics: 499-533. Springer (See the section about Hintikka’s contributions and the references therein)
  • Gochet P, Gribomont P (2006) Epistemic logic. In: Gabbay DM, Woods J (eds) Handbook of the History of Logic, vol 7

Other pointers:
About formal semantics and logic of questions (surveys):

  • D. Harrah: The logic of questions, Handbook of Philosophical Logic, Second Edition (D. Gabbay and F. Guenthner, eds.), vol. 8, Kluwer, Dordrecht/Boston/London, 2002, pp. 1–60.
  • A. Wiśniewski: Semantics of questions, Handbook of Contemporary Semantics. Second Edition (S. Lappin and C. Fox, eds.), Wiley-Blackwell, 2014.

About embedded question, factivity: 

  • P. ‎Egré: Question-embedding and factivity. Grazer Philosophische Studien 77(1) (2008) 85– 125

About Techniques and philosophy of Quantified modal (epistemic) logics:

  • Fitting, M., First-order intensional logic, Annals of Pure and Applied Logic 127 (2004), pp. 171-193.
  • Holliday, Wesley H. & Perry, John (2014). Roles, Rigidity, and Quantification in Epistemic Logic. In Alexandru Baltag & Sonja Smets (eds.), Trends in Logic, Outstanding Contributions: Johan van Benthem on Logic and Information Dynamics. Springer 591-629.
  • F. Belardinelli, A. Lomuscio, Quantified epistemic logics for reasoning about knowledge in multi-agent systems, Artificial Intelligence, Volume 173, Issues 9–10, June 2009, Pages 982-1013.
  • G. Corsi, E. Orlandelli: Free Quantified Epistemic Logics. Studia Logica 101(6): 1159-1183 (2013)

About concealed questions:

  • Maria Aloni and Floris Roelofsen. Interpreting Concealed Questions Linguistics and Philosophy 34(5), 443-478, 2011
  • Maria Aloni. Quantification under Conceptual Covers. PhD thesis University of Amsterdam, Amsterdam, 2001.

About Inquisitive semantics and Logic


Day 2 Knowing whether (Slides)

Main Ref:

Other pointers:

  • Ciardelli, I., Roelofsen, F.: Inquisitive dynamic epistemic logic. Synthese 192(6) (2015) 1643– 1687
  • M. Aloni, P. Égré, Tikitu de Jager: Knowing whether A or B. Synthese 190(14): 2595-2621 (2013)


Day 3: Logics of “knowing what” (slides)

Main Ref:


Day 4: Logics of “knowing how” (slides)

Main Ref:


Day 5: A general framework (slides)

Main Ref: