Abstract 

The talk is in two parts In the first part Michael Abraham will
introduce several examples of Talmudic Kal Vachomer reasoning and
examine its formal logical properties.  In the second part Dov Gabbay
will introduce a new method of abduction, Matrix Abduction, arising
from the first part, and apply it to modelling the use of
non-deductive inferences in the Talmud such as Analogy and the rule of
Kal Vachomer ( Argumentum A Fortiori.)

The basic model is as follows:

Given a matrix A with entries in {0, 1}, we allow for one or more
blank squares in the matrix, say ai,j =?. The method allows us to
decide whether to declare ai,j = 0 or ai,j = 1 or ai,j =?
undecided. This algorithmic method is then applied to modelling
several legal and practical reasoning situations including the
Talmudic rule of Kal-Vachomer. We also show that this new rule of
Matrix Abduction, arising from the Talmud, can also be applied to the
analysis of paradoxes in voting and judgement aggregation. In fact we
have here a general method for executing non-deductive inferences.

references:
Analysis of the Talmudic Argumentum A Fortiori
Inference Rule (Kal Vachomer) using Matrix Abduction
M. Abraham, D. Gabbay, U. Schild
Bar-Ilan University, Israel
and
King's College London, UK
3rd draft March 2009
Paper 338