The Return of the Syllogism

The Aristotelian syllogistic is known to do a good job of accounting
for the validity of inferences couched in a certain common fragment of
many natural languages. To take an example from English:

  Every man is a mortal
  Some philosophers are men
  -----------------------------
  Some philosophers are mortals.

As we might say in more technical terms: the collection of valid
syllogisms compiled by Aristotle constitutes a sound and complete
inference system for the fragment in question---a result which was
actually obtained by Łukasiewicz and Słupecki in the 1930s.

On the other hand, the expressive limitations of this fragment are all
too plain to see.  As Augustus De Morgan famously observed, it cannot
accommodate even the most elementary inferences involving relational
facts, for example:

  Every man is an animal
  ----------------------------------
  He who kills a man kills an animal.

In this talk, I shall show how contemporary techniques in
Computational Logic can be used to investigate the prospects for
providing a `natural logic' in the style of the Aristotelian syllogistic,
but without some of its expressive restrictions. These techniques
reveal a rich and varied proof-theoretical landscape, in which the
Aristotelian Syllogistic is one among many points of interest