Lecturers: Dr. Minghui Ma (Southwest University)
Dr. Mariko Yasugi (Kyoto University)
Date: 2013/01/17 11 : 00 –
＊11: 00-11:50 Mariko Yasugi ” Halting property of identification in the
limit–Along Dedekind’s thoughts on the domain extensions –”
＊12:00-13:00 Minghui Ma ”Semantic Analysis of Belief Sentences:
between qualitative and quantitative approaches”
At Seminar Room No. 12, Research Building No. 2, Kyoto University
(Building No. 34)
(1) Mariko Yasugi ” Halting property of identification in the limit–
Along Dedekind’s thoughts on the domain extensions –”
Given a recursive process of evaluating some values, there are three
possibilities. (We say a process terminates when it satisfies a
certain condition after finitely many steps.) The process terminates
and we will know the termination effectively, and hence we can obtain
the final value effectively; the process terminates but we cannot know
effectively where it does, and we can obtain the final value only
after infinitely many steps (so to speak); the process does not
terminate. The first case corresponds to general recursion, thatis,
the halting property, and the second case corresponds to limiting
recursion, that is, the identifiability in the limit.
Our purpose is to justify the view that the latter is in the
homogeneous nature of the former. To attain our purpose, we will
resort to Dedekind’s standpoint on the domain extensions as expressed
in his Habilitationsrede.
Our problem originates in dealing with discontinuous functions in
studying the computability structures in analysis.
(2) Minghui Ma “Semantic Analysis of Belief Sentences: between
qualitative and quantitative approaches”
There are two approaches to semantic analysis of belief sentences:
qualitative and quantitative. The modern qualitative approach was
probably first given by Frege in his analysis of indirect speech, and
later explicitly specified by Hintikka in his fundamental work on the
`Hintikka-style` (Kripke) semantics for knowledge and belief.
Hintikka’s approach, and the famous AGM theory and more recent
plausibility interpretation of belief are in the qualitative category.
The quantitative approach was probably first practiced in the Bayesian
interpretation of probability which can be seen as an extension of
logic that enables reasoning with propositions whose truth or falsity
is uncertain, i.e., with beliefs. My approach to belief is `between`
qualitative and quantitative approaches. Based on Kripke models,
natural numbers added to the epistemic range of states can be taken as
`degrees` or `weights` of belief, and so the semantics of belief can
be given in terms of comparing weights of propositions. Furthermore,
those weighted models can be used to analyze conditional belief.
Weighted models can also be applied to analyze more scenarios related
to counting problem. In this talk, some logics of reasoning about
belief will also be presented.