CAPE Truth theory and Logic Workshop

CAPE Truth theory and Logic Workshop

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 (京都大学総合研究2号館第8講義室)

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”

Shunsuke Yatabe (Kyoto University)
title: Yablo paradox and semantics of coinductive language
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
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?
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
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