[FOM] infinite logical derivations

Adam Kolany dr.a.kolany at wp.pl
Tue Aug 21 03:21:13 EDT 2007

Ron Rood wrote
> Dear FOM-ers,
> In a Hilbert or Gentzen-style logic, logical derivations are usually 
> represented as finite sequences of sentences.
> Are there studies of logics in the style of Hilbert or Gentzen (natural 
> deduction) which, in one way or another, allow for logical derivations 
> of infinite length? If yes, can you provide me with pointers to the 
> literature?


(google:  algorithmic logic salwicki mirkowska)

Algorithmic Logic is a formal system developed by A.Salwicki and
G.Mirkowska (polish logicians) , as I know, for proving properties of
programs and one of the rules (the one for while loop - which seems
obvious /page 105 - see the preview/) of the system is infinitary. There
are several books on that topic. most which I know are in polish. the
one I pointed above is the only one  in english about which I know.

regards, Adam K.


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