| Language |
English
|
| From |
2011/05/25 16:30
|
| To |
2011/05/25 17:30
|
| Place | Room 110, RIMS, Kyoto University |
| Seminar Name | Colloquium |
| Title |
Coalgebra, its Logic, and some of its Mathematical Environments |
| Field |
Analysis
Other
|
| Speakers | Yde Venema |
| Affiliation | RIMS & University of Amsterdam |
| Abstract | Computers and other electronic equipment are becoming more and
prominent, both in our daily life, and in society as a whole.
When we are confronted with undesired or incomprehensible behavior
of for instance our mobile phone, we will naively start reasoning
about the system, modelling it as a state-based evolving system,
that we can only observe as a black box.
Clearly, when it comes to specifying and reasoning about the
behavior of critical software systems, a sophisticated mathematical
theory is needed.
The theory of coalgebra, which has emerged from theoretical computer
science in the last two decades, provides a general, mathematical
framework for reasoning about such state-based evolving systems.
It combines mathematical simplicity with wide applicability, due to
its categorical foundations: many features such as input/output,
nondeterminism, probability, and interaction can be encoded in the
coalgebraic type which formally is a functor over Set (or some other
base category). Coalgebra allows us to give precise mathematical
definitions of notions such as behavior or observational equivalence
of systems. Logic naturally enters the picture since we want to
specify and reason about behavior in a formal way.
In the talk, we will give a very informal introduction and motivation
of coalgebra and coalgebraic logic. We then briefly explain the
dualities between algebra and coalgebra, and discuss the principle of
coinduction. In the second part of the talk we describe some of
the mathematical environments of the theory, and sketch how ideas
from coalgebraic logic can be used to generalize results in topology
(the Vietoris construction) and automata theory (Rabin's Theorem).
|
| Note | 16:00より RIMS 1階ロビーで tea
◆ 多数のご来聴をお待ちしております．
◆ とくに院生の出席を歓迎します． |
| Link | http://www.kurims.kyoto-u.ac.jp/ja/seminar/danwakai.html |
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