Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal-Vachomer) using Matrix Abduction

Reference : Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal-Vachomer) using Ma...


	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Computer science
	To cite this reference:	http://hdl.handle.net/10993/15950

Title :	Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal-Vachomer) using Matrix Abduction
Language :	English
Author, co-author :	Abraham, Michael [> >]
	Gabbay, Dov M. [King’s College London, Department of Computer Science, London, UK; Bar-Ilan University, Ramat-Gan, Israel]
	Schild, U. [> >]
Publication date :	2009
Journal title :	Studia Logica
Publisher :	Springer
Volume :	92
Issue/season :	3
Pages :	281–364
Peer reviewed :	Yes
ISSN :	0039-3215
e-ISSN :	1572-8730
City :	Berlin
Country :	Germany
Abstract :	[en] We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Ana- logy and the rule of Argumentum A Fortiori. 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 add an Appendix showing 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.
Permalink :	http://hdl.handle.net/10993/15950

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