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From: hah@ztivax.UUCP (Dr. Hans Hellendoorn)
Newsgroups: comp.ai
Subject: Re: K. T. Fann's thesis on abduction.
Summary: Aristotelian Logic
Message-ID: <5302@ztivax.UUCP>
Date: 24 May 91 08:26:34 GMT
References: <8409@uceng.UC.EDU>
Reply-To: hah@ztivax.UUCP (Dr. Hans Hellendoorn)
Organization: Siemens AG in Munich, W-Germany
Lines: 44

In article <8409@uceng.UC.EDU> skhadye@uceng.UC.EDU (Shankar P. Khadye) writes:
>I am reading Fann's thesis on Peirce's theory of abduction. In it,
>Fann has referred to Barbara, as in - " ... can be reduced to Barbara."
>and so on. Can anybody elaborate on it?
>
>	       ......Shankar P. Khadye

I can advise you to read the book of Jan Lukasiewisz, "Aristotle's
Syllogistic - from the standpoint of modern formal logic",
Oxford, Clarendon Press, 1951.

The Barbara is the most simple and well known syllogism, like
  All man are mortal,
  All Greeks are men,
     therefore
  All Greeks are mortal.

These are three A-sentences, therefore bArbArA. There are E, I
and O sentences too, forming moods like the Fesapo:
  All B is A
  No C is B
     therefore
  Some A is not C,

like the Fresison:
  Some B is A
  No C is B
     therefore
  Some A is not C,

and the well known Datisi, written in a style that better
corresponds to Aristotle's original texts:
  A belongs to all B
  C belongs to some B
     therefore
  A belongs to some C
  
A recent contribution on the field of syllogisms that I
found most interesting is from a Soviet scientist:
S.V. Chesnokov, "The Effect of Semantic Freedom in the
Logic of Natural Language", Fuzzy Sets and Systems
22(1987)121-154.

Hans Hellendoorn