Date:  February 13 (Wed)  9:00-17:00,

Place:  The 8th lecture room, “Research Bldg. No. 2 (Sougou Kenkyu 2-Goukan)” of Kyoto University, No34 of the map in

Timetable:

9:00-10:15 Shunsuke Yatabe “Yablo paradox and semantics of coinductive language”

10:30-11:45 Graham E. Leigh “Global reflection and theories of truth”

13:15-14:30 Katsuhiko Sano “What is the corresponding first-order

logic to coalgebraic modal logic?”

14:30-15:45 Leon Horsten ” One hundred years of semantic paradox”

16:00-17:15 Philip Welch “Alan Turing’s Mathematical work”

Abstracts:

Shunsuke Yatabe (Kyoto University)

title: Yablo paradox and semantics of coinductive language

Abstract: We generalize the framework of Barwise and Etchmendy’s “the

liar” to that of coinductive language, and focus on a difficulty of

constructing semantics. We define a game theoretic semantics, which can

be regarded as a version of Austin semantics.

Graham E. Leigh  (University of Oxford)

title: Global reflection and theories of truth

Abstract:

This talk explores the relationship between the global reflection

principle (“If A is provable, A is true”) and its arithmetic cousins

(“If A is provable then A”). I will provide a proof-theoretic analysis

of a number of axiomatic theories of truth expanded by transfinite

hierarchies of reflection principles.

Katsuhiko Sano (School of Information Science, Japan Advanced

Institute of Science and Technology)

title: What is the corresponding first-order logic to coalgebraic modal logic?

Abstract:

It is well-known that modal logic over Kripke models can be

regarded as the bisimulation-invariant fragment of first-order logic,

where the notion of bisimulation tells us when given two Kripke models

are `similar’ with each other. This is called Van Benthem’s

characterization theorem. The main aim of this talk is to propose a

corresponding first-order syntax with Van Benthem-style

characterization to coalgebraic modal logic, a uniform framework to

cover modal logic over Kripke models, modal logic over neighborhood

models, graded modal logic, probabilistic modal logic, etc. This talk

focuses on a conceptual background to explain our strategy of finding

a corresponding FO syntax for coalgebraic modal logic. A key idea

consists in Arthur Prior’s early idea of hybrid logic (esp. modal

operators for pointed truth) and C. C. Chang’s FO syntax for

neighborhood models. This talk is based on a joint work with Dirk

Pattinson (ANU), Tadeusz Litak (Friedrich-Alexander University of

Erlangen and Nuremberg (FAU)), and Lutz Schroeder (FAU).

Leon Horsten (University of Bristol)

title: One hundred years of semantic paradox

Abstract:

This article contains an overview of the main problems, themes and

theories relating to the semantic paradoxes in the twentieth century.

From this historical overview I tentatively draw some lessons about

the way in which the field may evolve in the next decade.

Philip Welch (University of Bristol)

title: Alan Turing’s Mathematical work