Dear Bruno, thanks for the good references, I will integrate them on the resource page (or on a separate page).
Some of these books I have already read (Boolos), others are on my list (Rogers). Smullyan's Forever Undecided is unfortunately out of print, but I am on the lookout for used copies ;-) Best Wishes and thanks for your time in thinking about the best references, Günther P.S.: I agree with you that the best way to convey knowledge is discussion - I will keep bugging you with questions concerning COMP and UDA *grin* Bruno Marchal wrote: > Günther, > > > AUDA is based on the self-reference logic of axiomatizable or > recursively enumerable theories, of machine. Those machines or theories > must be rich enough. In practice this means their theorems or beliefs > are close for induction.This is the work of Gödel and followers, notably > Löb, who found a nice generalzation of Gödel's theorem and Solovay who > proves the arithmetical completeness of the logic he will call G and G'. > Here is the key paper: > > Solovay, R. M. (1976). Provability Interpretation of Modal > Logic. /Israel Journal of Mathematics/, 25:287-304. > > I follow Boolos 1979 and Smullyan "Forever Undecided" in calling such > system G and G*. G has got many names K4W, PrL, GL. > There are four excellent books on this subject: > > Boolos, G. (1979). /The unprovability of consistency/. Cambridge > University Press, London. > > This is the oldest book. Probably the best for AUDA. And (very "lucky" > event) it has been reedited in paperback recently; I ordered it, and I > got it today (o frabjous day! Callooh! Callay! :). It contains a > chapter on the S4 intensional variant of G, and the theorem (in my > notation) that S4Grz = S4Grz*. The first person is the same from the > divine (true) view and the terrestrial (provable) view. > I have it now in three exemplars but two are wandering. > > Boolos, G. (1993). /The Logic of Provability/. Cambridge University > Press, Cambridge. > > This is the sequel, with the Russians' solutions to virtually all open > problems in Boolos 1979. The main problem was the question of the > axiomatizability of the first-order extension of G and G* (which I note > sometimes qG and qG*). And the answers, completely detailed in Boolos' > book, are as negative as they can possibly be. qG is PI_2 complete, and > qG* is PI_1 complete *in* the Arithmetical Truth. The divine > intelligible of Peano Arithmetic is far more complex than Peano > Arithmetic's ONE, or God, in the arithmetical interpretation of Plotinus. > > > Smoryński, P. (1985). /Self-Reference and Modal Logic/. Springer Verlag, > New York. > > I have abandon this one sometimes ago, because of my eyes sight defect, > but with spectacles I have been able to distinguish tobacco product from > indices in formula, and by many tokens, it could be very well suited for > AUDA. The reason is that it develops the theory in term of (computable) > function instead of assertions, showing directly the relation between > computability and SIGMA_1 provability. Nice intro from Hilbert's program > to Gödel and Löb's theorem, and the Hilbert Bernays versus Löb > derivability conditions. It contains a chapter, a bit too much blazed in > the tone, on the algebraic approach to self-reference, which indeed > initiates originally the field in Italy (Roberto Magari). > It contains also chapter on the Rosser intensional variants. > > Smullyan, R. (1987). /Forever Undecided/. Knopf, New York. > > This is a recreative introduction to the modal logic G. I was used some > times ago in this list to refer to that book by FU, and I don't hesitate > to use some of Smullyan's trick to ease the way toward self-reference. > It helps some, but can irritate others. > Note that Smullyan wrote *many* technical books around mathematical > self-reference, Gödel's theorems in many systems. > > Modal logic is not so well known that such book can presuppose it, and > all those books introduce modal logic in a rather gentle way. But all > those books presuppose some familiarity with logic. Boolos Et Al. is OK. > It is difficult to choose among many good introduction to Logic. By some > aspect Epstein and Carnielly is very good too for our purpose. > > Note that the original papers are readable (in this field). All this for > people who does not suffer from math anxiety which reminds me I have to > cure Kim soon or later. The seventh step requires some math. AUDA > requires to understand that those math are accessible to all universal > machine 'grasping" the induction principle, this is the work of Gödel > and Al. > > I think the book by Rogers is also fundamental. Cutland's book is nice, > but it omits the study of the Arithmetical Hierarchy (SIGMA_0, > PI_0, SIGMA_1, PI_1, SIGMA_2, PI_2, ...). > > > AUDA without math = Plotinus (or Ibn Arabi or any serious and rational > mystic). Roughly speaking. > > I will think about a layman explanation of AUDA without math, and > different from UDA. > > Best regards, > > Bruno > > > > > On 25 Jan 2009, at 18:45, Günther Greindl wrote: > >> >> Hi Bruno, >> >>>> Goldblatt, Mathematics of Modality >>> Note that it is advanced stuff for people familiarized with >>> mathematical logic (it presupposes Mendelson's book, or Boolos & >>> Jeffrey). >>> >>> Two papers in that book are "part" of AUDA: the UDA explain to the >>> universal machine, and her opinion on the matter. >> >> I would like to add a "guide to AUDA" section on the resources page. >> Maybe you could specify the core references necessary for understanding >> the AUDA (if you like and have the time)? >> >> Here a first suggestion of what I am thinking of: >> >> Boolos Et Al. Computability and Logic. 2002. 4th Edition >> >> Chellas. Modal Logic. 1980. >> >> Goldblatt, Semantic Analysis of Orthologic and >> Arithmetical Necessity, Provability and Intuitionistic Logic >> to be found in Goldblatt, Mathematics of Modality. 1993. >> >> >> >> What do you think? >> >> Best Wishes, >> Günther >> >> >> > > http://iridia.ulb.ac.be/~marchal/ > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
