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A Dynamic Logic Seminar in Beijing, April 2009

Minghui MA (Department of Philosophy, Tsinghua University, Beijing, P. R. China)

In April 2009, Professor Johan van Benthem gave a mini-workshop on six current research topics in logical dynamics at Tsinghua University (Beijing). The workshop also included three presentations by local students on their own logic research, plus two related lectures by Prof. van Benthem at other universities in Beijing. The workshop concluded with a ‘surprise topic’: see below – followed by a lively informal discussion with the students about their experiences in the Chinese educational system. We hope that the following gives an impression of what happened during the last three weeks.

Prof. van Benthem gave an introduction to all six topics from 15:00 to 17:00 on April 8 and 9, against the background of his 6-week “Logical Dynamics” seminar at Tsinghua last autumn (2008). Next, presentations were given by six local students, who first read relevant papers from students in Amsterdam and Stanford, and then prepared talks, in correspondence with the authors.

April 15, 15-16:00. Merging Dynamic Logic of Observation and Inference. Ruizhi Yang a PhD student at the Center for Logic, Language and Cognition of Peking University discussed Fernando Velazquez-Quesada’s solution for merging explicit and implicit knowledge in dynamic epistemic logic (DEL) with acts of inference that do not eliminate worlds, but increase ‘access’ to them. The main restriction in this merged system is that only factual formulas in the propositional language are involved in explicit actions of ‘awareness’ update. Yang’s new proposal was to add one more dynamic awareness operation, allowing the agent to drop obsolete higher-order facts.

April 15, 16-17:00. Logic of Questions. Li Ma, also a PhD student at the Center for Logic, Language and Cognition of Peking University presented Stefan Minica’s ideas on logic of questions, including a draft axiomatization of a public question logic with public announcements added. Some problematic features of the system found in the discussion suggested that it does not yet have the right form: question modalities seemed to drop out where they should not. This may be connected to getting clearer on a general issue that was raised in the discussion: what a ‘logic of questions’ is supposed to achieve.

April 16, 15-16:00. DEL, Protocols and Formal Epistemology. Jun Zhang from Beijing Technology University presented the combination of DEL, protocols from epistemic temporal logics (ETL), and applications to formal epistemology, which has been developed by Tomohiro Hoshi in his current Stanford dissertation, to be defended this spring. He introduced the topic with a famous story of Zhuangzi in ancient China about knowing the thoughts and feelings of fish. After then he concentrated on PAL-generated ETL-models through repeated public announcements that obey state-dependent protocols. In discussion, we tried to get a sense for the epistemological import of this.

April 16, 16-17:00. Formal Learning Theory and DEL. Minghui Ma, a PhD student at the philosophy department of Tsinghua University presented bridges between formal learning theory and DEL that have been especially studied by Nina Gieraczymczuk. He first introduced formal learning theory: new to us (though we learnt that people in the philosophy of science center at Tsinghua had studied it). He then explained Nina’s ideas on how to model finite identification in DEL. He raised two questions. One is to give an axiomatization of the logic of learnability, and the other is to explore the meaning of the word ‘learn’ in natural language, and thus merge learning more closely with DEL.

April 22, 15 – 16:00. Dynamic Doxastic Logic and Doxastic Temporal Logic. Junhua Yu, a graduate student at the department of philosophy of Tsinghua University, presented the relations between dynamic doxastic logic of beliefs and doxastic temporal logic from a manuscript by Prof. van Benthem and C. Degremont. The presentation explained the analogy with work by van Benthem, Gerbrandy, Hoshi and Pacuit. relating DEL and ETL, (that goes back to work by van Benthem and Fenrong Liu). In the discussion some background information emerged about these two main streams of modeling agent interaction, and the point of doing ‘framework comparisons’.

April 22, 16-17:00. Backward Induction. Manvel Rincon-Cruz from Harvard University, a visiting student at Tsinghua University, presented the logical analysis of rationality in backward induction by Baltag, Smets and Jonathan Zvesper. This work continues a line starting with Aumann, using a new notion of ‘dynamic rationality’, and Manvel explained the proofs of some theorems that provide sufficient conditions for the backward induction outcome in terms of common knowledge of persistent general belief in rationality. He also raised the question of finding both necessary and sufficient condition for the backward induction outcome. In discussion, the question came up to which extent this solution solves the original ‘Paradox of Backward Induction’

The following are three additional sessions about research by local people.

8 April, 13-14:30. Graded Modal Frame Definability. Minghui Ma presented his research in graded modal logic, in particular, the definability of elementary frame classes via a Goldblatt-Thomason type theorem for the graded modal language. He gave definitions of ‘graded ultrafilter extension’, graded p-morphism and graded bisimulation, and tries to approximate the model-theoretic proof of the theorem for basic modal logic. Discussion topics were the definition of graded ultrafilter extension, and the algebraic background for Goldblatt-Thomason theorem.

15 April, 13-14:30. Self-referentiality. Junhua Yu presented his work on the issue of self-referentiality in the realization procedure for S4 derivations in the labeled proof system LP (Logic of Proofs). After a quick introduction to LP, a counter-example was given to a proof-theoretic conjecture of Kuznets about the source of self-referentiality, and next, a necessary condition was given for self-referentiality together with another one for direct-self-referentiality. During the subsequent discussion, the intuitive meaning of self-referentiality in various semantics for LP was probed.

22 April, 13-14:30. Sheffer Stroke and Modal Logic. Fangfang Tang, a faculty member at CASS (Chinese Academy of Social Sciences) presented the work in her Tsinghua PhD dissertation. Her topic is analytic modal proof systems based on a generalized sheffer stroke. She presents analytic systems for the modal logics K and S4, which are variants of cut-free modal tableaus or Gentzen systems, while using hypersequents for S5. This is a modal version of work by Zhang Qingyu and Liu Xinwen (both from CASS) for first order logic. Afterwards, we discussed what it really means to be ‘more efficient’ or ‘automatizable’, and whether cut-free systems are not really a theoretical tool, say, for proving (uniform) interpolation theorems. Also, a new reference emerged that seemed relevant: Nguyen Anh Linh’s Studia Logica 2001 paper ‘Analytic Tableau System and Interpolation for Modal Logics KB, KDB, K5, KD5’.

23 April, 15-17:00. Logic and Space. Prof. van Benthem presented a surprise topic to conclude the workshop. He discussed the historical relationship between logic and space, a neglected area, that has been put on the map anew in the Handbook of Spatial Logic. Two central examples from the 1930s are Tarski’s formalization and decidability proof for elementary geometry, and the other are Tarski’s theorems saying that the modal logic of topological spaces is S4, but even that of just the real numbers. Reviving the former direction, Andreka and Nemeti have given a Tarski-style analysis of Minkowski space and relativity theory. Reviving the second tradition, Mints and Wolter analyzed topological spaces with an additional operator for continuous maps, that can result in very high complexity.

Other Lectures. Prof. van Benthem also gave two related logic lectures at Beijing. One is ‘A Logical Perspective on Solving Games’ at the Logic Center of Renmin University, from 14:30 to 17:00 on 17 April. The other is ‘Logical Dynamics of Information Flow’ at the Institute of Philosophy of CASS, from 10:00 to 11:30 on 21 April.

For moire information on the seminar, please visit https://sites.google.com/site/dynamicsbj2009/

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