Hi Wei,

>The interlibrary loan department of my local library finally came through
>and found a copy of "The Logic of Provability" for me. I think I've read
>enough of it to at least try to understand AUDA now. What should I read at
>this point? (To make sure I'm on the right track, your G and G* correspond
>to Boolos's GL and GLS, right?)


Yes, G is GL (Godel-Lob) and G* is GLS (Godel-Lob-Solovay). G has plenty 
of
names (K4W, PRL, etc.). G and G* are the more common name. The use of the
star "*" is useful because it can be generalised for all the modal systems
in my work (cf, Z ; Z*, Z1 ; Z1*, X1 ; X1*, etc.).

If you have read enough of Boolos 1993, including the S4-preserving
treatment of provability, and the Visser Logics V and V* (or GLV and GLVS)
I guess you should be able to understand at least formally my post:
http://www.escribe.com/science/theory/m2855.html
An important paper is the one by Goldblatt 1974 on his translation of
quantum logic in the B modal logical system.

But I would insist that it is preferable to understand the UDA before
the AUDA. Your last conversation with Hall Finney makes me
suspect that you *do* have a "problem" with the self-duplication thought
experiment and/or the 1-3 person pov distinction.
UDA is much more simple than AUDA (except for the professionnal logician).
To be honest I have not understand your answers to Hal Finney last posts,
I agree with Hall's remark though).


>BTW, Bruno, I think you've probably wasted a lot of time trying to explain
>provability logic to people on this list. 
>You should have just told us to go read that book.


I did that! But when George Levy asked me for some details, I have
not resisted giving elementary background. 
I realise Logic is less well known than I was used to think. 


>But even the book assumes familiarity with a lot of
>background knowledge. What book would you recommend to someone who has
>taken just one quarter of introduction to logic and one quarter of
>introduction to theory of computation in college?


A shortcut is  Jeffrey "Formal Logic, its scope and limit"
               Boolos and Jeffrey "Computability and Logic".
I will give you more precise ref asap.


>I'm curious about a couple of other things. How many people in the world
>claim to understand AUDA? 


Mathematicians and computer scientists I met have no problems in
understanding AUDA. So I know at least a dozen of mathematicians who have
understand it. (Of course I must still publish it in an "international
serious journal"). Comparing to the logician standard the AUDA is 
quite easy,  although it leads quickly to difficult mathematical 
questions.
 
UDA is more difficult but only because we must forget or abstract from
more than 2000 years of Aristotelian Substancialism, I guess.
And UDA is the main motivation for the AUDA.

What is perhaps hard with my thesis is that it belongs at the 
intersection of cognitive science, physical science and mathematical
logic.


>How did you get interested in provability logic?


My "child" goal was: answering "what is the life-time of an 
amoeba?" from an amoeba point of view. (I was fond of amoeba
and protozoans).
I have hesitated between biology and chemistry for solving
that problem until I discovered Godel's proof and the use of
diagonalisation
for defining rigorously the needed forms of self-reference.
(cf also  http://www.escribe.com/science/theory/m3412.html).


Happy New Year!

Bruno

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